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Abstract
Interpretation of analgesic and antipyretic responses documented after paracetamol administration is confused because response is not directly related to concentration in the blood, but rather to an effect compartment. The effect compartment does not have real measurable concentrations, but concentrations equate approximately to those observed in the cerebrospinal fluid. A time delay exists before drug reaches the effect compartment, and the equilibration half-time between the central and effect compartment is described by a single first-order parameter (Teq or T1/2keo), reported to be ∼1 h for paracetamol. Paediatric analgesic studies are limited because they have only explored postoperative pain after tonsillectomy or day-stay surgery. Other pain types and pain confounders have not been investigated. Adult studies are also similarly limited. Studies investigating antipyresis have not explored the maximum response, limiting the precision of any EC50 estimate. The influence of the cyclical nature of fever or initial temperature is seldom accounted for in antipyretic studies. Target effect compartment concentrations of 5 mg/l for fever and 10 mg/l for pain do not seem unreasonable on the basis of current literature. Speed of onset may be shortened by giving a larger initial dose or improving absorption characteristics. Consequent plasma concentration achieved, differences in effect compartment equilibration times, and the shape of the effect compartment concentration–response curve help to explain differences between common analgesic/antipyretic drugs.
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Measurement of plasma drug concentrations can provide useful information. It enables doctors to make treatment decisions toward achieving therapeutic concentrations and managing patients suffering an overdose. Concentration measurements enable new formulations of drugs to be registered with regulatory authorities on the basis of bioequivalence. These measures are a prerequisite in the development of new drugs, as the pharmacokinetic information obtained contributes substantially to the determination of dose and dosing interval. If sufficient information is available about relationships between plasma or serum concentrations and therapeutic effect, then determination of speed of onset and comparisons of different drugs become easier. However, interpretation of plasma or serum drug concentrations is not always straightforward. The objective of this review is to examine some of the issues and make some observations with specific reference to one of the most widely available and commonly used antipyretic and analgesic drugs, paracetamol (acetaminophen).
Paracetamol is said to be an effective antipyretic at plasma concentrations of 10–20 mg/l.1 However, the paper by Rumack,1 which is often cited as the source of these antipyretic plasma concentrations, provides no data and only refers to an unpublished source. Several papers have documented a time delay of 1–2 h between maximum plasma concentrations (Cmax) and maximum temperature reduction.2 3 It is reasonable that a time delay should occur, given that the effect site for antipyresis is the hypothalamus, which must induce physiological body change to cause temperature reduction. Fever associated with prostaglandin E-like activity in the cerebrospinal fluid (CSF) has been shown to be abolished by paracetamol, but the drug had no effect on fever that was not mediated by prostaglandins.4 As the plasma time–concentration profile of paracetamol administered orally is a semi-bell shaped, or rising and falling, curve, a single concentration or range of observed concentrations can be obtained from either side of the curve. To make sense of this, additional information is necessary: when was the sample obtained in relation to dosing and how long after dosing does Cmax occur (Tmax)? A concentration of 10 mg/l, for example, may be found both before and after Cmax. This spot concentration of 10 mg/l after Tmax may be associated with greater fever reduction than the same concentration before Tmax. Conversely, a spot concentration of 10 mg/l that is associated with the absorption phase may occur before the maximum effect. A concentration of 10 mg/l during absorption may be associated with some effect; the drug has “started to work”, although maximum effect has not yet been achieved (fig 1).
The nature of the relationship between plasma concentration of paracetamol and analgesia has also resulted in conflicting interpretations. Prescott5 makes reference to a range of “probably about 5–20 mg/l”, but acknowledges that there are few studies in which drug concentrations and analgesic effects have been measured simultaneously in man. Seymour and Rawlins6 were unable to find a clear relationship between analgesia and plasma concentrations of paracetamol in 11 adults undergoing extraction of the third molar. The sequential (in time) plots of pain scores against plasma concentrations showed marked clockwise hysteresis (a looping of the curve due to a lag between plasma concentration and effect). In contrast, using a laser-induced pain model, Nielsen et al7 found a relatively good direct correlation between pain threshold changes and plasma concentrations, despite a lag time consistent with that reported by Seymour and Rawlins.6 A minimum therapeutic plasma concentration is not quoted in this paper, but visual examination of the plots suggests that significant differences in pain thresholds occur by 1 h, in association with a plasma concentration of 12 mg/l. A hysteresis effect was possibly not observed because of the limited range of paracetamol concentrations and response scores.
Two studies in children have reported increasing analgesia with increasing dose and/or plasma concentration. Anderson et al8 assessed paracetamol analgesia in children undergoing tonsillectomy. At 30 min after the end of surgery, a pain score (visual analogue scale, 0–10) was obtained and a venous blood sample was taken for analysis of plasma paracetamol concentration. Children given paracetamol elixir had a higher mean (SD) paracetamol concentration (22.6 (9.1) vs 7.6 (4.5) mg/l, p<0.001) and a lower median visual analogue scale (VAS) pain score (5 vs 7, p<0.02) than those who were given suppositories. Korpela et al9 studied day-stay children randomised to receive a single dose of 0, 20, 40 or 60 mg/kg rectal paracetamol after induction of anaesthesia. In the post-anaesthesia care unit, pain scores were significantly lower in the 40 and 60 mg/kg groups than in the placebo and 20 mg/kg groups. The calculated rectal dose of paracetamol at which 50% of the children did not require a rescue opioid was 35 mg/kg.
Time delays between paracetamol concentrations and analgesic effect have been reported in adult volunteers7 10 and children.11 These time delays mean that there is not a direct relationship between concentration and effect. Paracetamol must move from the plasma to an effect compartment where it has its physiological influence (fig 2).
UNDERSTANDING THE CONCENTRATION–EFFECT RELATIONSHIP
The effect compartment model
A sequential plasma concentration–effect plot forms a clockwise hysteresis loop because of this delay in effect. Hull et al12 and Sheiner et al13 introduced the effect compartment concept for muscle relaxants. The effect compartment concentration is not the same as the blood or plasma concentration and is not a real measurable concentration. It is modelled on the assumption that it has negligible volume and contains negligible blood. This enables determination of a single first-order parameter, a rate constant (Keq or Keo), that describes movement of drug into this effect compartment. The derived parameter, Teq or T1/2keo,
describes the equilibration half-time between central and effect compartments. This mathematical trick assumes that the concentration in the central compartment is the same as that in the effect compartment at equilibration, but that a time delay exists before the drug reaches the effect compartment. Equilibration may not be reached after a single dose and may, in some cases, take considerable time even after repeat dosing. The time delay may be very short (fentanyl group of analgesic drugs) or may take days to weeks (antidepressants). Once a peak concentration in the effect compartment is reached, the concentration falls. This decline may or may not occur in parallel with a decline in the central compartment, depending on T1/2keo. The concentration in the effect compartment is used to describe the concentration–effect relationship.
The relation between effect compartment drug concentration and effect may be described by a hyperbolic curve according to the sigmoid Emax equation:
This equation was originally devised to describe the haemoglobin dissociation curve.14 E0 is the baseline measure of the variable of interest such as temperature or pain score, Emax is the maximum effect change, Ce is the concentration in the effect compartment, EC50 is the concentration producing 50% Emax, and N is the Hill coefficient defining the steepness of the concentration–response curve. The drug concentration in the effect compartment may have a different magnitude of response depending on the concentration. For example, at high concentration, further increases in concentration may have little effect because the curve has reached the “ceiling”. Small increases in concentration at the steep part of the curve will produce dramatic changes in effect, whereas at low concentration there may be little gain before the inflection point is reached. A small N (<1) results in rapid onset of effect but a shallower curve, and it takes longer to achieve Emax. A large N results in more rapid achievement of Emax; a very high value results in an all-or-nothing effect, and thus, within a very narrow concentration range, the response goes from all to nothing or vice versa.
Brown et al15 have reported a linked pharmacokinetic–pharmacodynamic (PK-PD) model for febrile children given oral paracetamol with a mean (SE) Teq of 71 (7) min. The Teq for an analgesic effect compartment in children undergoing tonsillectomy was shorter, at 53 min (coefficient of variation 217%) min.11 When data from the latter study are fitted to the Emax model, in which the greatest possible pain relief (measured with a VAS of 0–10) is an Emax of 10, an actual Emax of 5.17 (coefficient of variation 64%) and an EC50 of 9.98 (coefficient of variation 107%) mg/l was estimated.11 Table 1 shows the relationship between effect site concentration and analgesia after tonsillectomy.11 This effect compartment–response relationship for tonsillectomy pain is shown in fig 3A, and fig 3B shows the hysteresis curve generated by plotting the plasma concentration against pain relief. The temporal relationships for plasma concentration, effect compartment concentration and analgesic effect after oral administration of 12.5 mg/kg paracetamol given to a typical 8-year-old child after tonsillectomy are shown in fig 3C.
The indirect-response (turnover) model
Many drug actions are mediated through the synthesis or elimination of a physiological substance. The concentration at the site of drug effect either stimulates or inhibits the rate of production or elimination of the physiological substance (response variable). Indirect response models, rather than hypothetical effect compartment models, may be more appropriate for drugs when time lags exist between plasma or biophase drug concentrations and the time course of pharmacodynamic responses.16 The indirect response model has implications that go beyond distribution models and may be useful in the interpretation and prediction of pharmacodynamic events that are not necessarily due to distributional effects, but rather affect onset and loss of response. The link models are not appropriate when response Emax or EC50 changes with dose or response is governed by turnover—that is, the rate-limiting step is the turnover of response and not distribution of drug to and from the biophase.17
Paracetamol effect is mediated centrally through a cyclo-oxygenase effect on prostaglandin synthesis18 and would be suitable for this type of model exploration. This model has yet to be investigated for paracetamol.
INTERPRETING THE LITERATURE
Antipyresis
Wilson et al2 studied 9 and 12 mg/kg paracetamol given orally to children with fever due to otitis media or upper respiratory tract infection. There were 10 and eight subjects respectively in each group. Blood samples were taken over 5 h, as were rectal, oral and axilla temperatures. The maximum antipyretic effect occurred when plasma concentrations of paracetamol were declining (ie, hysteresis). The therapeutic plasma concentration for paracetamol identified in this study was in the range 4–18 mg/l, but the equilibration half-time and effect compartment concentrations were not quantified.
Brown and colleagues15 used previously reported data from 178 febrile children treated with single oral doses of ibuprofen (5 or 10 mg/kg), paracetamol (12.5 mg/kg) or placebo, to create a linked PK-PD model for these treatments. Rectal temperatures were taken, and plasma samples analysed for up to 12 h after drug administration. The effect compartment concentration of paracetamol that provided 50% of the maximum effect in this model was 4.63 mg/l. On visual inspection by Brown et al of the efficacy–time profiles of the febrile children, for 91 of 102 children given paracetamol, the addition of a slope and/or a sinusoidal cyclic function to the Emax component was required to fit the data satisfactorily. These additional functions were required to describe the baseline temperature, which, if left untreated, rises and falls. A slope and/or cyclic function was also required in the pharmacodynamic model for all 22 children given a placebo. In addition, the magnitude and rate of the temperature fall in children with high fevers were greater than that in children with mild fever; temperature is unlikely to fall below 37°C. The aetiology of pyresis may also affect the rate of fever reduction, the magnitude of which may be partially due to the underlying disease, although this has not been investigated. In some cases, the cyclic function of the baseline fever may be explained by temperature regulation. Regardless of the causes of the shifting baseline (eg, underlying pathology, physiological homoeostatic regulation), both confound analysis of drug action and make the simple, unmodified Emax effect model less than satisfactory for interpretation of antipyretic drug effects. The influence of the initial temperature on the magnitude of antipyretic drug response also has a major impact on pharmacodynamic investigations of antipyretic drugs. There are possibly other, as yet unexplained, covariables that could be taken into account when developing appropriate dosing regimens for these antipyretics in febrile children. In addition, doses above 12.5 mg/kg were not explored, and the authors were therefore unable to explore the maximum anti-pyretic effect (Emax), which creates uncertainty in the estimate of the true efficacy of paracetamol.
Analgesia
Interpretation of analgesic data can be complicated by factors unrelated to drug concentration. Placebo effect, waxing and waning of pain, cultural values, time of day, maturation of pain pathways, and psychological interpretation of pain and lack of equivalence of pain-rating systems19 all affect the relationship between drug concentration and pain relief. Data from adult studies are consistent with the effect site concentration–response described in children.
The relationship between analgesia and plasma concentration of paracetamol in 11 subjects undergoing extraction of the third molar showed marked clockwise hysteresis.6 Adult human studies have been performed in volunteers in whom experimental pain was induced by brief cutaneous application of argon laser pulses and the analgesic effect assessed as change in pricking pain threshold.7 10 Pain threshold was significantly raised compared with placebo 1 and 2 h after paracetamol ingestion. Maximum analgesia occurred 1 h after peak plasma concentrations.
This delay between Cmax and maximum analgesia is consistent with an effect compartment, and concentrations in this effect compartment mirror closely those in the CSF. Paracetamol concentrations in the CSF peaked at 2 h (Teq 2.1 h) after intravenous administration of a paracetamol prodrug (propacetamol) in a study by Bannwarth et al20 in adult patients with rheumatic and nerve root compression pain. Hydrolysis of propacetamol to paracetamol is rapid, and the Teq is an accurate reflection of the equilibration half-time between plasma and CSF compartments. Van der Marel et al21 investigated children (n = 41) 1 week to 18 years of age undergoing surgery for placement or revision of a ventriculoperitoneal shunt or insertion of a temporary external ventricular drain. Weight (a determinant of size) determined Teq changes with age in children. The authors predicted, using allometric scaling,22 that a neonate (3.5 kg), a 1-year-old child (10 kg), a 5-year-old child (20 kg), a 10-year-old child (30 kg) and an adult (70 kg) would have a Teq of 0.9, 1, 1.4, 1.6 and 1.93 h, respectively. This prediction was based on the concept that time-related indices in an individual (Ti), such as heart rate, respiratory rate or drug half-times, can be scaled for size to a size standard (eg, 70 kg person, Wstd) using an exponent of ¼ applied to weight22:
The difference between small and large animals is that smaller animals have faster physiological processes and consequently a shorter life span. A power function of ¼ can be derived for pharmacokinetic half-times based on basic pharmacokinetics applied to allometric predictions of clearance and volume:
Onset of effect will therefore be quicker in small children than in large children or adults.
Hahn et al23 investigated the analgesic effect of intravenous paracetamol in 64 female patients with postoperative pain. Each patient was given a bolus dose after elective laparoscopic surgery, with four groups receiving 10, 20 or 40 mg/kg or placebo in a random fashion. For the first hour after dosing, there was no difference between groups in the amount of rescue alfentanil patient-controlled analgesia (PCA) administration. Between 1 and 2 h, significantly more rescue alfentanil was consumed by the placebo group than in any of the paracetamol groups, but there was no difference between the paracetamol groups—that is, no dose–response was seen in terms of rescue opioid use for paracetamol. The authors concluded that a ceiling effect of paracetamol may be present at a plasma concentration of 14 mg/l. These data are consistent with the delayed effect model and the shape of the effect site–response curve (fig 3A)—that is, as concentration increases, the slope of the curve for analgesic response becomes less steep—consistent with fig 3A.
The pharmacokinetics and analgesic effectiveness of rectally administered paracetamol was examined by Beck in 65 women undergoing hysterectomy.24 Pain was measured on a VAS, and PCA morphine consumption was also assessed. Two doses of paracetamol (20 and 40 mg/kg) were compared with a combination of diclofenac 100 mg/kg and paracetamol 20 mg/kg. The data show slow absorption of paracetamol after rectal administration, with a Tmax of ∼4 h. The higher dose of paracetamol did not result in lower pain scores or decreased PCA. The 40 mg/kg dose resulted in a maximum plasma concentration of 17.2 mg/l; the 20 mg/kg dose correspondingly gave 10.4 mg/l. The authors concluded that plasma concentrations reported to reduce fever (10–20 mg/l) were only achieved at the higher dose (40 mg/kg) after rectal administration. The lack of improved analgesia with the 40 mg/kg dose led to the supposition that analgesic plasma concentrations may be higher than those required for antipyresis. However, as mentioned above, the antipyretic plasma concentrations were from a source that provided no data and only referred to an unpublished source.
Effective analgesic concentrations may be higher than those required for fever control, but comparison is difficult because the effect compartment concentration–response relationship for both antipyresis and analgesia has not been fully explored. The EC50 of 4.63 mg/l for antipyresis is reported to be lower than that for analgesia (EC50 9.98 mg/l).11 15 Observations from the study of Beck et al24 in adults are, however, consistent with the paediatric PK-PD model for analgesia after tonsillectomy.11 The slow absorption of rectal paracetamol is mirrored by a slow rise in effect site concentrations, and it would be easy to misinterpret a direct relationship between plasma concentration and analgesic effect before peak concentration (fig 4A,B). The difference in minimum pain scores on a VAS scale of 0–10 (6.8 vs 7.5) is small, and, given the large between-patient variability of pharmacodynamic parameters, we might not expect a clinical difference between patients given either dose.
MANIPULATIONS TO INCREASE SPEED OF ONSET
Patients seek rapid relief from symptoms, be they pain or fever. The simplest method to decrease time to onset of effect is to increase the dose. The study by Korpela et al9 shows a linear relationship between increasing rectal paracetamol dose and analgesia, with statistical significance reached at 40 and 60 mg/kg doses when compared with placebo. Maximum plasma paracetamol concentration is directly proportional to dose for drugs with first-order absorption and elimination. Target effect compartment concentrations (and effect) will be reached earlier as dose is increased. The administration of a large initial “loading” dose to achieve the target concentration speedily is commonly used in medicine.
An increase in speed of absorption will also speed up the onset of action. Paracetamol has a pKa of 9.5, and, in the alkaline medium of the duodenum, paracetamol is largely non-ionised. Consequently, absorption of the non-ionised form from the duodenum to the systemic circulation is rapid (mean (SD) T1/2abs 6.8 (0.9) min in adult volunteers).25 Absorption within the stomach is minimal, and the limiting step for paracetamol absorption is gastric emptying into the duodenum. Consequently, a pharmacokinetic model using a first-order input model (T1/2abs) with a lag time (Tlag) that accounts for the delay in reaching the duodenum has been used to describe absorption. Brown et al26 have reported rapid absorption (mean (SE) T1/2abs 2.7 (1.2) min; Tlag 4.2 (0.4) min) in febrile children given elixir orally. Similar absorption parameters have been estimated in children given paracetamol as an elixir before tonsillectomy (T1/2abs 4.5 min, coefficient of variation 63%, Tlag 0).11 Absorption may be altered by formulation. An intravenous formulation has direct access to the central compartment. Tablets and capsules must disintegrate and then dissolute, introducing a lag time before duodenal uptake. Food slows absorption by delaying gastric emptying. The rectal absorption of suppositories is slow, and onset of maximum effect is delayed when paracetamol is given by this route. Age also has an impact. Oral absorption in children under the age of 3 months was delayed by a factor of 3.68.27 Gastric emptying is slow and erratic in the neonate.28 Normal adult rates may not be reached until 6–8 months of age.29
Formulation also affects speed of absorption. Soluble formulations have an enhanced onset of activity in adults.30–33 The salts of non-steroidal anti-inflammatory drugs (eg, lysine, arginine, potassium) are more rapidly absorbed than free acid formulations and also have a faster onset time in patients with dental pain.30 A paracetamol formulation containing sodium bicarbonate has enhanced gastric emptying and disintegration/dissolution compared with conventional tablets. The differences in gastric emptying are more pronounced in the fasted state, and the differences in disintegration are more pronounced in the fed state.34–37 In adults with sore throat, this formulation has been shown to provide significant analgesia compared with placebo from 15 min after dosing.38 Effect compartment concentrations were not estimated, but reported plasma concentrations of 15–20 mg/l and analgesia onset at 15 min suggest satisfactory equilibration with the effect compartment. The benefit of these new formulations in children is uncertain because absorption of elixir in children is already rapid and any increase in absorption will possibly have minor effect only.
Non-steroidal anti-inflammatory drugs may have a more rapid speed of onset than paracetamol because of a smaller Teq. Mandema and Stanski39 studied adult patients (n = 522) given a single oral or intramuscular dose of placebo or a single intramuscular dose of 10, 30, 60, or 90 mg ketorolac for pain relief after orthopaedic surgery. Pain relief was found to be a function of drug concentration (Emax model) and time (waxing and waning of placebo effect). The EC50 and Teq were 0.37 mg/l and 24 min. This Teq for ketorolac in adults is smaller than that reported for paracetamol in children.11 We might expect a smaller ketorolac Teq in children, on the basis of allometric scaling.22 The age of the cohort studied influences speed of observed onset.
The slope function of the sigmoid Emax equation (Hill coefficient, N) will also affect speed of onset. A small N results in rapid onset of effect, but it takes longer to achieve Emax when compared with a larger N (fig 5). The pharmacodynamic models for paracetamol analgesia and antipyresis both used a Hill coefficient of 1.11 15 It is possible that they may differ because the investigators fixed the Hill coefficient to 1 in each case to ensure stability of the models; it was not possible to explore other Hill coefficients. The effect compartment–response relationships for paracetamol in pain may be different from those in fever. The EC50 for antipyresis (4.63 mg/l)15 is reported to be half that for analgesia (9.98 mg/l).11 This may explain the rapid reduction of fever by almost 1°C within 30 min after oral paracetamol (elixir formulation, 15 mg/kg) seen in 150 febrile children (fig 6).
Table 2 summarises the effect of these parameter changes. The simplest method for increasing speed of onset is to increase the dose. We have used an effect site concentration of 5 mg/l paracetamol as a target concentration in table 3. This concentration is associated with pain reduction of 1.7 units and is similar to the EC50 for antipyresis.
CONCLUSIONS
Plasma paracetamol concentrations depend on the route of administration, volume of distribution, and clearance. Despite characterisation of the time–concentration relationship, a single-point plasma concentration imparts limited information about the relationship between concentration and effect. It is the concentration in the effect compartment rather than in the plasma that relates to the effect. Although the concentration in the effect compartment may mirror the plasma concentration, this effect compartment concentration is subjected to time delays, and the maximum effect compartment concentration is less than the maximum plasma concentration after a single dose. The time delays are dependent on body size, being shorter with decreasing body size, characterised by weight.
Relationships between this effect compartment paracetamol concentration and analgesia and antipyresis have been described using sigmoid Emax models. Paediatric analgesic studies are limited because they have only explored postoperative pain after tonsillectomy or day-stay surgery. Other pain types and pain confounders have not been investigated in children, and there are only limited studies in adults. Studies investigating antipyresis have not explored Emax, limiting the precision of any EC50 estimate. The potential confounding effect of the cyclical nature of fever and the initial temperature are seldom accounted for in antipyretic studies. A minimum target effect compartment concentration of 5 mg/l for fever and 10 mg/l for pain do not seem unreasonable on the basis of current literature. Some effect will be observed at lower concentrations because the response is part of a continuum, not an all-or-nothing phenomenon.
In biostudies where the exact time of dosing is known and repeated sampling is conducted, speed of onset of antipyretic effect and speed of onset of analgesic effect could be inferred from the time taken to achieve plasma concentrations of 5 mg/l and 10 mg/l, respectively. Speed of onset may be shortened by giving a larger initial dose or improving absorption characteristics. Differences in effect compartment equilibration times, the shape of the dose–response curve (dictated by N, Emax and EC50), and where on this curve the concentration is acting help to explain differences between antipyretic or analgesic effects.
Acknowledgments
We thank Professor L Prescott for his review and suggestions.
REFERENCES
Footnotes
Competing interests: Support was provided solely from institutional and/or departmental sources. IG is employed by Reckitt Benckiser Healthcare International, Nottingham, UK. Figure 6 was provided from data submitted for publication by Reckitt Benckiser Healthcare International.