Clinical Pharmacokinetics

, Volume 47, Issue 2, pp 139–146

Relevance of Absorption Rate and Lag Time to the Onset of Action in Migraine

Authors

  • Hugo J. Maas
    • Leiden/Amsterdam Center for Drug ResearchLeiden University
  • Marc A. H. Spruit
    • Leiden/Amsterdam Center for Drug ResearchLeiden University
  • Meindert Danhof
    • Leiden/Amsterdam Center for Drug ResearchLeiden University
    • Leiden/Amsterdam Center for Drug ResearchLeiden University
    • Clinical Pharmacology & Discovery MedicineGlaxoSmithKline
Original Research Article

DOI: 10.2165/00003088-200847020-00007

Cite this article as:
Maas, H.J., Spruit, M.A.H., Danhof, M. et al. Clin Pharmacokinet (2008) 47: 139. doi:10.2165/00003088-200847020-00007

Abstract

Objective: The objective of this analysis was to simulate the performance of oral triptan formulations with varying absorption characteristics and their impact on the onset and magnitude of the antimigraine effect using a Markov model for migraine attacks.

Analysis: Sumatriptan pharmacokinetic data were obtained from clinical pharmacology studies in which marketed solid formulations were administered. Based on a population pharmacokinetic model, mean concentration-time profiles were generated by varying the absorption rate constant and lag time. Subsequently, the simulated profiles were evaluated in a disease model of migraine to predict the onset and duration of the effect (the pain-free, pain-relief response).

Results: Based on a therapeutic dose of 50 mg of sumatriptan, a maximum gain in the pain-free response of 12% was achieved with an increased absorption rate. This gain in the response was reached approximately 0.5 hours after administration. A decrease only in the lag time with respect to the currently available formulations (i.e. 0.24 hours) resulted in a maximum gain of 5% in the pain-free response, which in contrast may not be interpreted as clinically relevant.

Conclusion: Model-based predictions suggest that increases in the absorption rate of the currently marketed oral formulation of sumatriptan result in a gain in the pain-free response that is both clinically and statistically relevant.

Background

Sumatriptan is used as an effective drug for abortive treatment of migraine attacks.[1] However, a considerable number of migraineurs are not pain free or do not obtain pain relief within 2 hours post-dose.[2] This emphasizes the need for fast onset of action, which can be achieved by the development of formulations with increased release and absorption profiles. Currently, several of those formulations are available (e.g. sumatriptan rapid-release tablets,[3,4] and rizatriptan and zolmitriptan orally disintegrating tablets[5,6]). Development of formulations with increased release and absorption profiles is not limited to the field of migraine treatment. For example, ibuprofen, a widely used NSAID, is available in a liquigel formulation (capsules containing liquid medication) to facilitate a fast onset of pain relief.[7]

However, modification of pharmacokinetic properties assumes an immediate correlation between exposure and response. In migraine, very little work has been performed to establish that relationship, since the pain response during an attack has important time dependencies, which make the characterization of the concentration-effect curve rather difficult.[810] Recently, we have applied a model-based approach to migraine headache that allows one to assess and predict the onset and magnitude of the treatment effect of triptans.[11]

In clinical development, studies aimed at evaluating the pharmacokinetics of new formulations usually include a weighted parameter (e.g. the area under the plasma concentration-time curve [AUC]), the maximum plasma drug concentration (Cmax) and the time to reach the Cmax (tmax) as primary endpoints, ignoring the underlying drivers of the absorption process, which should be primarily parameterized in terms of an absorption rate constant (ka).

In fact, the relevance of using a model-based approach to assess the impact of pharmacokinetic properties on the response has been highlighted in a recent publication by Troconiz et al.,[12] in which the treatment response to a non-triptan migraine drug was described using a logistic regression model. According to the authors, increasing the ka from 0.34 h−1 to 6 h−1 plays a minor role in terms of the improvement in pain relief at 2 hours. In their simulations, the pain relief response was also dependent on the dose and bioavailability. Notably, it was found that increasing the absorption rate resulted in a gain of more than 20% in the response when the highest dose level was simulated in conjunction with low values of bioavailability (0.2). However, this gain was largely lost at higher values of bioavailability.

In the present study, simulations were performed to investigate which absorption characteristics are required to show clinically significant improvement in the onset of action of sumatriptan. The parameters describing the absorption characteristics included the lag time and the ka of the first-order absorption process. The influence of either of these parameters on the response was assessed. This approach illustrates how disease modelling can be used to support the rationale for the development of new formulations and accurately quantify the benefits of novel dosage forms. In conjunction with bioequivalence data, disease modelling provides evidence of the impact of drug delivery properties on the pharmacokinetics and pharmacodynamics.

Methods

Pharmacokinetic Model

A two-compartment population pharmacokinetic model was developed, based on the structural model proposed by Cosson and Fuseau[13] using NONMEM V software (Globomax LLC, Hanover, MD, USA). Parameter estimates were obtained by fitting the model without additional covariate effects to clinical data from 513 subjects who were given single oral doses of marketed solid formulation of sumatriptan (dose range 2.5–100 mg) [figure 1]. A summary of the final model parameters is shown in table I. The results of the pharmacokinetic analysis were used in the subsequent simulations of the response.
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Fig. 1

Sumatriptan pharmacokinetic data from phase I and II studies (n = 513). Oral doses ranging from 2.5 mg to 100 mg were used to estimate parameters for the pharmacokinetic model. The symbols represent the observed plasma concentrations, and the solid lines depict the model predictions (the population curve). For reference, a population-averaged concentration-time profile of a subcutaneous (SC) administration of sumatriptan 6 mg is shown in red.

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Table I

Pharmacokinetic parameter estimates of the reference formulation, based on the nonlinear mixed effects model by Cosson and Fuseau[13] a

To study the effect of the absorption process on the model-predicted pain response, pharmacokinetic profiles were characterized by varying the values of the first-order ka following a sumatriptan dose of 50 mg or 100 mg. Based on a reference estimate of 0.49 h−1 for ka, values of 0.25, 1.28 and 2.56 h−1 were considered for this analysis. These values represent half of the ka of the marketed oral formulation and approximately 1- and 2-fold the ka of the absorption process after subcutaneous administration, respectively.

Subsequently, we evaluated the relevance of the lag time on the model-predicted pain response by varying the lag time of the first-order absorption process in the pharmacokinetic model under the assumption of a constant reference ka value. The population estimate of the lag time for the marketed oral formulation was found to be 0.24 hours. The simulated lag times included 0.12, 0.48 and 0.96 hours. These values reflect 2-fold and 4-fold changes in release, which we believe to be a realistic range of values for oral formulations.

As variability in the pharmacokinetic profiles is generally large, it was important to include it in the prediction of the headache response. Means and confidence intervals (CIs) for the time courses of the concentrations were calculated using Box-Cox transformations.[14] Means and 95% CIs were then chosen to represent the degrees of pharmacokinetic variability and used as input functions for the response model.

Response Model

A hidden Markov model (HMM)[15] has recently been developed to predict headache responses during a migraine attack.[11,16] This model consists of a hidden layer representing an unobserved disease process. State-to-state transition dynamics within the hidden layer are determined by transition rates. This layer also represents the level at which sumatriptan exerts its activity. Quantification of the treatment response was enabled by including sumatriptan concentrations as a continuous covariate in the model. The action of sumatriptan on forward transition rates was assumed to follow a maximum effect (Emax) model.[17] A second layer in the model, the open layer, couples the response states to the observed pain scores. The number of states in this layer was set to three, which is equal to the number of clinically identifiable response states: no relief, pain relief and pain free. These states include scores that are based on a four-point categorical pain rating scale. The shifts in pain scores represent different pain intensity levels, which are clinically translated as pain relief and pain-free status.[18] The starting point is score 2 or 3 (no relief); if the pain intensity reaches 0 or 1, pain relief is said to occur; if the pain intensity reaches 0, the pain-free state is reached. Figure 2 illustrates the HMM topology used.
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Fig. 2

Diagram of the hidden Markov model for a migraine attack. The thick red arrows indicate transitions affected by drug treatment. A migraine attack starts in state 1. For the pain scores: 0 = no pain; 1 = mild pain; 2 = moderate pain and 3 = severe pain.

Model Fitting

Model parameters were estimated for both layers of the HMM using open-source HMM software[19] running within S-Plus on a Linux workstation (SuSE Linux 9.0 with kernel 2.4.25-4GB-SMP). The Emax model was incorporated into the HMM as a user-written model specification file. Details of the method and the results of disease modelling (including parameter estimates) have been presented and discussed previously.[11,20] Using the simulated pharmacokinetic profiles associated with different ka and lag time values, the mean pain-free and pain-relief responses, including 95% CIs, were calculated using an implementation of the Kolmogorov algorithm.[20]

Evaluation of Model Performance

The significance of differences in the response for the different pharmacokinetic profiles was evaluated by comparison with the CIs of the reference formulation. This consisted of determination of the timepoints at which the CIs of a competing scenario did not overlap those of the reference. Within the range of significant differences, the largest value was defined as the most significant gain in the response. The corresponding timepoint was defined as the time of the most significant gain in the response. For accurate interpretation of the simulation results, pharmacodynamic variability was incorporated into the analysis to account for additional variation in the response originating from the pharmacodynamic model.

Results

Absorption Rate

The effect of the ka on the pain response was investigated for four different ka values and at two dose levels (50 mg and 100 mg). The concentration-time profiles corresponding to these ka values after a dose of 100 mg are shown in figure 3. It can be observed that the tmax is reached earlier with an increasing ka. These profiles were used as the input function for the response model. To account for the role of pharmacokinetic variability in the potential range of responses, three scenarios were identified that reflected (among other factors) the impact of between-subject variability in oral clearance: responses based on low, mean and high exposure. The impact of changes in the absorption rate on the pain-free response following a 100-mg dose of sumatriptan is depicted in figure 4 a. As the absorption rate increases, the response increases until a time is reached after which this relationship is reversed; i.e. a slight decrease in the response is observed. Placebo response curves are also displayed to demonstrate the superiority of all sumatriptan formulations. For simplicity, the variability in the response parameters is not displayed in figure 4. For reference, the pain-free levels at 2 hours for the mean exposure level were 5%, 21%, 27%, 32% and 32% for placebo and for formulations with increasing ka levels of 0.25, 0.49, 1.28 and 2.56 h−1, respectively.
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Fig. 3

Log(concentration)-time plots including 95% CIs for (a) ka = 0.25 h−1, (b) the reference oral formulation with ka = 0.49 h −1, (c) ka = 1.28 h−1, (d) ka = 2.56 h−1, for sumatriptan 100 mg. The mean and 95% confidence levels are referred to in the text as mean, low and high exposure levels, respectively.

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Fig. 4

(a) Predicted pain-free response after sumatriptan 100 mg for various absorption rates at low, mean and high exposure levels. (b) Predicted pain-free response after sumatriptan 100 mg for various lag times at low, mean and high exposure levels.

Table II summarizes the timepoints associated with the highest significant gain in the response between the reference formulation and formulations with varying absorption rates, for all doses and response types under evaluation. The expected minimum, mean and maximum gains at these timepoints are given in table III. The largest gain was observed for the pain-free response at a ka of 2.56 h−1 for sumatriptan 50 mg at the high exposure level. This indicates that an increase in the absorption rate can cause an increase of up to 12% in the fraction of patients responding by 30 minutes after administration.
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Table II

Timepoints of the largest significant gains in the pain-free and pain-relief response. Comparisons were made between the standard oral formulation (ka = 0.49 h−1) and hypothetical formulations of sumatriptan with ka values of 0.25, 1.28 and 2.5 h−1

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Table III

Gains in the pain-free and pain-relief response at the time of maximum significance (see table II). Comparisons were made between the standard oral formulation (ka = 0.49 h−1) and hypothetical formulations of sumatriptan with ka values of 0.25, 1.28 and 2.56 h−1 for sumatriptan doses of 50 mg and 100 mg, assuming low, mean and high exposure levels

The time course of the differences in the pain-free response attributable to the variation in absorption rates relative to the reference oral formulation (ka = 0.49 h−1) are plotted in figure 5. This figure shows the response profiles for sumatriptan 100 mg associated with the mean pharmacokinetic exposure derived from ka values of 0.25, 1.28 and 2.56 h−1. The gains are most significant at approximately 1 hour after administration (indicated by arrows).
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Fig. 5

Influence of changed absorption rates on the pain-free response to sumatriptan 100 mg at the mean exposure level. The thickened line segments indicate a significant difference. The arrows indicate the timepoint of the maximum significant difference, which was determined taking into account the variability in the response (pharmacodynamic) model. ka = absorption rate constant.

Lag Time

A similar sensitivity analysis was performed to study the influence of the lag time on the treatment response. The resulting pain-free response for the 100-mg dose is plotted in figure 4 b. In contrast to the effect of absorption rates, with an increasing lag time, the time versus response curves shift to the right, ultimately converging at 6 hours after administration. The maximum gain in the response and the timepoint of its occurrence were calculated for the test formulations with varying lag times. All gains were considerably smaller than those reached by varying the absorption rate. The largest significant gain (minimum, mean, maximum = 4%, 4%, 5%, respectively) was observed with a lag time of 0.12 hours at 0.25 hours after administration. This indicates that a reduction in the lag time relative to the standard formulation can increase the fraction of patients responding to treatment by up to 5%. This difference can be detected around 0.25 hours after administration.

Discussion

A major requirement for optimal treatment of migraine is fast pain relief. When treating migraine headaches, fast pain relief is the main quality desired by patients.[2125] Triptans (serotonin 5-HT1B/D receptor agonists) have proven efficacy in aborting migraine attacks. While the timing of treatment is crucial in abortive therapy, intervention early in an attack carries the risk of inappropriate dosage.[26] On the other hand, if the onset of action is delayed, the migraine headache may worsen and become untreatable.[8] This drives the need for formulations with optimal delivery properties.

The relevance of the dosing time can be mitigated by immediate release and availability of the drug at the site of action. In fact, this is assured by subcutaneous or intranasal administration. However, these have a number of disadvantages. Subcutaneous administration is inconvenient because of its invasive nature, whereas intranasal formulations are also less preferred by patients, and correct delivery of the drug can be an issue.[27] Combined with a higher patient preference for the oral dosage form, this line of reasoning warrants improvement in the delivery profiles of oral formulations.

In this study, a sensitivity analysis based on a pharmacokinetic-pharmacodynamic model of the antimigraine effects of triptans (sumatriptan) was done to assess which pharmacokinetic parameter contributes most to the increase in the response and time of onset. The response model on which these simulations were based describes the progression of pain during a migraine attack. Starting from moderate or severe pain intensity, patients experience relief over time, both through the natural progression of migraine and through the response to drug treatment. Disease progression is expressed as two consecutive transitions between three disease states, with transitions leading to less severe states being promoted by the presence of a triptan. These triptan-induced transitions correspond to the attainment of pain relief and pain-free status, respectively. Based on the properties of the Markovian process and experimental findings, it seems that sumatriptan acts more potently on the first transit rate, which is clearly related to the pain relief status.[11,28] We expect, therefore, that any improvement in drug delivery will mainly affect the pain-free response.

Oral delivery profiles are better characterized by the pharmacokinetic parameters ka and lag time, as compared with non-parametrical estimates of the Cmax and tmax. To identify the relationship between the ka and the response rate, four physiologically relevant values of ka were evaluated in our analysis. Two of these (1.28 and 2.56 h−1) were larger than the ka of the marketed oral formulation and one (0.25 h−1) was smaller. This range covers the absorption rates of most of the available sumatriptan formulations, varying from suppository to subcutaneous administration.[28] Similarly, four values of the lag time were evaluated, two larger than the lag time of the marketed oral formulation (0.48 and 0.96 hours) and one smaller (0.12 hour). This range was selected to capture physiologically relevant boundaries, namely oral administration of a solution and gastric stasis.

In migraine, time dependencies are a relevant component of the overall variability in the response. Therefore, an accurate description of the role of extrinsic factors, such as formulations, must take variability aspects into account. Pharmacodynamic variability was included in the analysis when testing the significance of the mean responses from different ka or lag time values relative to those of the reference formulation. This variability was expressed as 95% CIs around the mean responses. Two mean responses were defined as being significantly different if their CIs did not overlap. On the other hand, we incorporated pharmacokinetic variability into the evaluation of the response by considering three different exposure levels (low, mean and high exposure) for every ka and lag time.

By increasing the ka, we observed a maximum gain in the pain-free response of 12% at 0.5 hours post-dose after a 50-mg dose. This can be explained by the fact that at 0.5 hours, plasma concentrations are equivalent to the potency (50% effective concentration; EC50) value on the concentration-effect curve. At this point, the response is most sensitive to changes in concentration. Although with an increasing absorption rate, the responses initially increase, this may result in lower exposures at later timepoints, with a consequent reduction in the response (figure 4a). In fact, the response of the reference formulation is significantly different from the alternative hypothetical formulations only up to 2 hours after administration (figure 5, thickened line segments). Our findings coincide with reported clinical data. In the case of the 2-hour pain-free response after a 100-mg dose of marketed sumatriptan, the model-predicted rates varied from 12% to 50%, with a placebo rate of 6%. Literature values are 17% to 50%, with a placebo rate of 7%.[29]

Furthermore, our analysis revealed that decreasing the lag time with respect to the reference value of 0.24 hours is not as efficient as a change in the ka. A maximum gain of 5% was predicted for the 0.12-hour lag time formulation at the upper limit of exposure. Given the short lag time of the reference formulation and the existence of a physiological lower limit to the lag time, there is little room for improvement in this parameter. However, the value for the reference formulation was based on an analysis of data from healthy volunteers. In migraine patients, the absorption lag time may be prolonged by the presence of gastric stasis.[30] We cannot quantify whether additional changes in the lag time can be achieved.

From a theoretical perspective, gastric stasis during attacks may potentially affect various absorption parameters. Boyle et al.[31] reported that gastric emptying rates were delayed during severe or moderate attacks in 14 migraineurs. However, they did not evaluate the impact of this delay on sumatriptan absorption. Based on their findings, it is difficult to say which absorption parameters could be affected. In contrast, Cutler et al.[32] observed a “slight delay” in the absorption of sumatriptan during migraine attacks. However, from a comparison of the pharmacokinetics in healthy volunteers and patients during and outside an attack, Cosson and Fuseau[13] concluded that “migraine does not seem to affect the part of absorption described by first-order input, but rather the starting time of the zero-order input which is delayed in patients.” In both healthy volunteers and patients, the zero-order absorption process starts after the onset of the first-order process.[13] The impact of this extra delay is not completely clear, although it can be argued that the starting time of the first-order absorption process is crucial for the onset of the treatment response, as it occurs prior to the zero-order component. In the current article, it was assumed that the first-order process is the main determinant of the onset of the response, and therefore changes in the zero-order absorption rate were disregarded.

The role of gastric stasis on bioavailability also seems inconclusive. Whereas Cosson and Fuseau[13] did not detect any effect on bioavailability in their analysis, Hussey et al.[33] reported that the bioavailability of oral sumatriptan tablets in patients during a migraine attack is decreased by about 20%. This means that for the purposes of our simulations, the bioavailability would have been 12% instead of 15%. This absolute difference can be considered small and should not affect any of the conclusions of the article.

Our analysis was performed assuming that the concentration versus effect relationship is constant under all absorption conditions. At high absorption rates, the concentration-effect relationship might vary, since the earlier availability of the drug at the site of action may affect central sensitization and have repercussions on the later stages of the attack.

Conclusion

It can be concluded that increasing the absorption rate of the standard oral formulation of sumatriptan results in a gain in the pain-free rate that is both clinically and statistically significant. We recommend use of a model-based approach to explore new formulations and use of the ka as a parameter of interest for comparison of data and interpretation of changes in the delivery rate of antimigraine drugs.

Acknowledgements

This manuscript is part of a PhD research fellowship programme sponsored by GlaxoSmithKline, UK. GlaxoSmithKline had no further role in the research rationale, collection, analysis and interpretation of the data in the final contents of the manuscript submitted for publication. The authors have no conflicts of interest that are directly relevant to the content of this study.

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