A Markov approach to characterizing the PK-PD relationship of anti-migraine drugs Maas, H.J.

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relationship of anti-migraine drugs

Maas, H.J.

Citation

Maas, H. J. (2007, June 5). A Markov approach to characterizing the PK-PD relationship of anti-migraine drugs. Retrieved from

https://hdl.handle.net/1887/12040

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The relevance of absorption rate and

lag time to the onset of action and

pain relief in migraine

HJ Maas, M Spruit, M Danhof, OE Della Pasqua Submitted to J. Contr. Release

The purpose of this analysis was to simulate the performance of oral formulations with varying absorption characteristics and their impact on onset and magnitude of anti- migraine effect using a Markov model for migraine attacks.

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 (pain free, pain relief response).

Based on a therapeutic dose of 50 mg a maximum gain in pain free response of 12% was achieved with increasing absorption rate. This increase in response is reached approximately 0.5 h post-dose. A decrease only in lag time with respect to the currently available formulations (i.e., 0.24 h) resulted in a maximum gain of 5% in pain free response, which in contrast may not be detected as clinically relevant, given the high variability in placebo response in migraine trials.

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

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5.1 Introduction

Sumatriptan is used as an effective drug for abortive treatment of migraine attacks [1].

However, a considerable group of migraineurs is not pain free or reaches pain relief within two 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 absorp- tion profiles. Currently, several of those formulations are available (e.g. sumatriptan rapid-release tablets [3, 4], 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 non- steroidal anti-inflammatory drug, is available in a liquigel formulation (capsules contain- ing liquid medication) to facilitate fast onset of pain relief [7].

However, modification of pharmacokinetic (PK) properties assumes an immediate correlation between exposure and response. In migraine, very little work has been performed to establish that relationship, since pain response during an attack has important time dependencies, which make the characterisation of the concentration-effect curve rather difficult ([8, 9, 10]). Recently, we have applied a model-based approach for migraine headache that allows one to assess and predict the onset and magnitude of treatment effect for triptans [11].

In clinical development, studies aimed at evaluating the pharmacokinetics of new formulations usually include a weighted parameter (e.g. AU C0−τ, the maximum drug concentration (Cmax) and the time of maximum drug concentration (T max) as primary endpoints; ignoring the underlying drivers of the absorption process, which should be primarily parameterised in terms of an absorption rate constant (Ka).

In this study, simulations were performed to investigate which absorption characteristics are required to show clinically significant improvement of the onset of action.

Parameters describing the absorption characteristics included lag-time and absorption rate. The influence of either of these parameters on response was assessed. The 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 pharmacokinetics and pharmacodynamics.

5.2 Materials and Methods

5.2.1 Pharmacokinetic model

A two-compartment population pharmacokinetic model was developed based on a publication by Cosson and Fuseau [12] using the NONMEM V software (Globomax LLC, Hanover MD). Parameter estimates were obtained by fitting the model without additional covariate effects to clinical data from 513 subjects who were administered single doses of sumatriptan, dose range 2.5 – 100 mg (Figure 5.1).

To study the effect of the absorption process on model-predicted pain response, phar-

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macokinetic profiles were characterised by varying the values of the first-order absorption rate constant Ka following a dose of 50 and 100 mg sumatriptan. Based on a reference Ka estimate of 0.49 h⁻¹, absorption rate included values of 0.25 h⁻¹, 1.28 h-1 and 2.56 h⁻¹. These values represent half of the Ka of the marketed oral formulation, and approximately one- and twofold the Ka of the absorption process after subcutaneous administration, respectively.

Subsequently, we evaluated the relevance of lag time on model-predicted pain response by varying lag time in the PK model under the assumption of a constant reference Ka value. The population estimate of lag time for the marketed oral formulation was

time (h)

Conc (ng/ml)

0.1 1 10 100 1000

0 2 4 6 8

2.5 mg 5 mg 10 mg 20 mg 25 mg 30 mg 40 mg 50 mg 100 mg 6 mg sc

Figure 5.1:Sumatriptan PK data from phase I and II studies. The marketed oral formulations ranging from 2.5 mg to 100 mg were used to estimate parameters for the PK model.

Estimates for bioavailability were obtained from the additional use of subcutaneous data (the mean concentration profile of 6 mg subcutaneous data is shown).

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found to be 0.24 h. Simulated lag times included 0.12 h, 0.48 h and 0.96 h. These values reflect twofold and fourfold changes in release, which we believe to be a realistic range of values for oral formulations.

As variability in PK profiles is generally large, it was important to include it in the prediction of headache response. Mean and confidence intervals for the time courses of concentration were calculated using Box-Cox transformations [13]. Mean, 5% (lower) and 95% (upper) confidence levels were then chosen to represent the degrees of PK variability and used as input functions for the response model.

5.2.2 Response model

A hidden Markov model (HMM) [14] has been recently developed to predict headache responses during a migraine attack [11]. This model consists of a hidden layer represent- ing 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 treatment response was enabled by including sumatriptan concentrations as continuous covariate in the model. The action of sumatriptan on forward transition rates was assumed to follow an Emax [15] model. 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, 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 trans- lated as pain relief and pain free status [16]. The starting point is score 2 or 3 (no relief);

if pain intensity reaches 0 or 1, pain relief is said to occur; if pain intensity reaches 0, the pain free state is reached. Figure 5.2 illustrates the HMM topology used.

0 1 2 3

2 3

1

0 1 2 3

open layer:

scores

hidden layer:

states

Figure 5.2:Diagram of the hidden Markov model for a migraine attack. Bold arrows indicate transitions affected by drug treatment. A migraine attack starts in state 1.

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5.2.3 Model fitting

Model parameters were estimated for both layers of the HMM using open-source HMM software [17] 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. Using the simulated PK profiles associated with different Ka and lag time values, mean pain free and pain relief responses including 95% confidence intervals were calculated using an implementation of the Kolmogorov algorithm [18].

5.2.4 Evaluation of model performance

The significance of differences in response for the different PK profiles was evaluated by comparison with the confidence intervals of the reference formulation. This consisted in determining the time points at which the confidence intervals of a competing scenario did not overlap the reference’s. Within the range of significant differences, the largest value was defined as the most significant gain in response. The corresponding time point was defined as the time of most significant gain in response.

5.3 Results

5.3.1 Absorption rate

The effect of absorption rate constant on 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 5.3. It can be observed that the time of maximum concentration (T max) is reached earlier with increasing absorption rate constant. These profiles were used as input function for the response model. To account for the role of pharmacokinetic variability in the potential range of responses, three scenarios were identified: responses based on low, mean and high exposure. The impact of changes in absorption rate on pain free response following a 100 mg dose of sumatriptan is depicted in Figure 5.4. As the absorption rate increases, response increases until a time is reached after which this relation is reversed, i.e., a slight decrease in response is observed. Placebo response curves are also displayed to demonstrate superiority of all sumatriptan formulations.

Table 5.1 summarises the time points associated with the highest significant gain in response between reference formulation and formulations with varying absorption rates, for all doses and response types studied. The expected minimum, mean and maximum gains at these time points are given in Table 5.2. The largest gain was observed for the pain free response at an absorption rate of 2.56 h⁻¹ for 50 mg sumatriptan at the high exposure level. This indicates that an increase in absorption rate can cause an increase in the fraction of patients responding by up to 12% already 30 minutes after dosing.

The time course of the differences in pain free response attributable to the variation in absorption rates relative to the reference oral formulation (Ka=0.49 h⁻¹) are plotted

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Figure 5.3:Log(concentration)-time plots including confidence intervals for (a) Ka=0.25 h⁻¹, (b) 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. 5%, mean and 95% levels are referred to in the text as low, mean and high PK level, respectively.

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Table 5.1: Post-dose time (in hours) associated with the largest significant gain in pain free and pain relief response. Comparisons were made between standard oral formulation (Ka=0.49 h⁻¹) and hypothetical formulations with absorption rates of 0.25, 1.28 and 2.56 h⁻¹ for doses of 50 and 100 mg sumatriptan, assuming low, mean and high exposure levels.

Pain free Pain relief Dose PK exposure Ka (h⁻¹) Ka (h⁻¹)

0.25 1.28 2.56 0.25 1.28 2.56

50 mg low 1.6 1.6 1.7 0.0 1.0 0.9

mean 1.3 1.1 1.0 0.6 0.6 0.7

high 0.7 0.4 0.5 0.5 0.4 0.5

100 mg low 1.8 1.6 1.6 1.0 0.9 0.9

mean 1.1 0.9 0.8 0.5 0.5 0.6

high 0.4 0.3 0.3 0.0 0.0 0.4

in Figure 5.6. This figure shows the response profiles for sumatriptan 100 mg associated with the mean PK exposure derived from absorption rate values of 0.25, 1.28 and 2.56 h⁻¹. Gains are most significant at approximately 1 hour post-dose (indicated by arrows).

5.3.2 Lag time

A similar sensitivity analysis was performed to study the influence of lag time on treatment response. The resulting pain free response for the 100 mg dose is plotted in Fig- ure 5.5. In contrast to the effect of absorption rates, with increasing lag time the time vs response curves shift to the right, ultimately converging at 6 h after dosing. The maximum gain in response and the time point of its occurrence were calculated for the test formulations with varying lag times. All gains were considerably smaller than those reached by varying absorption rate. The largest significant gain (min, mean, max = 4%, 4%, 5%) was observed with a lag-time of 0.12 h at 0.25 h after dosing. This indicates that a reduction in 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 h after dosing.

5.4 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 [19, 20, 21, 22, 23]. Triptans (5-HT1B/1D receptor agonists) have proven efficacy in aborting migraine attacks. Whilst in abortive therapy the timing of treatment is essential, intervening early

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percentage of patients

0 2 4 6 8

0 20 40 60 80 100

low PK level

Placebo Ka=0.25/h Ka=0.49/h Ka=1.28/h Ka=2.56/h

0 2 4 6 8

0 20 40 60 80 100

mean PK level

time (h)

0 2 4 6 8

0 20 40 60 80 100

high PK level

Predicted pain free response after placebo and sumatriptan 100 mg for different absorption rates

Figure 5.4: Pain free response after 100 mg sumatriptan for various absorption rates at low, mean and high PK levels.

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0 2 4 6 8

0 20 40 60 80 100

low PK level

Placebo lag time=0.12 h lag time=0.24 h lag time=0.48 h lag time=0.96 h

0 2 4 6 8

0 20 40 60 80 100

mean PK level

time (h)

0 2 4 6 8

0 20 40 60 80 100

high PK level

Predicted pain free response after placebo and sumatriptan 100 mg for different lag times

Figure 5.5:Pain free response after 100 mg sumatriptan for various lag times at low, mean and high PK levels.

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in an attack carries the risk of inappropriate dosing [24]. On the other hand, if the onset of action is delayed, migraine headache may worsen and become untreatable [8]. This drives the need for formulations with optimal delivery properties.

The relevance of dosing time can be mitigated by immediate release and availability of 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 by its invasive nature, whereas intranasal formulations have shown vari- able bioavailability [25]. Combined with a higher patient preference for the oral dosage form [25], this line of reasoning warrants the need to improve delivery profiles of oral formulations.

In this study, a sensitivity analysis based on a PK-PD model for the anti-migraine effects of triptans was to assess which PK parameter contributes most to the increase of response and time of onset. The response model upon which these simulations were based describes progression of pain during a migraine attack. Starting from moderate or severe pain intensity, patients experience relief over time, both through natural progression

Figure 5.6:Influence of changed absorption rate on pain free response for 100 mg sumatriptan at mean PK level. Bold segments indicate a significant difference. Arrows indicate the time point of maximum significant difference.

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Table 5.2: Gain in pain free and pain relief response. Gain in pain free and pain relief response (min, mean, max; as percentage of patients) at time of maximum significance (see Table 5.1). Comparisons were made between standard oral formulation (Ka=0.49 h⁻¹) and hypothetical formulations with absorption rates of 0.25, 1.28 and 2.56 h⁻¹doses of 50 and 100 mg sumatriptan, assuming low, mean and high exposure levels. The highest gain is indicated in bold.

Pain free Pain relief

Dose PK exposure K a (h⁻¹) K a (h⁻¹)

0.25 1.28 2.56 0.25 1.28 2.56

50 mg low 0 , -1 , -2 1 , 2 , 3 2 , 3 , 4 0 , 0 , 0 1 , 4 , 6 4 , 6 , 8 mean -1 , -2 , -3 1 , 2 , 3 2 , 3 , 4 0 , -1 , -3 1 , 2 , 3 1 , 3 , 4 high -3 , -5 , -6 4 , 6 , 7 4 , 8 , 12 0 , -1 , -2 0 , 1 , 1 1 , 1 , 2 100 mg low -1 , -2 , -3 2 , 3 , 4 3 , 5 , 6 0 , -3 , -5 2 , 4 , 6 4 , 6 , 9 mean -2 , -3 , -4 3 , 4 , 6 5 , 6 , 8 0 , -1 , -2 0 , 1 , 2 1 , 2 , 3 high -3 , -4 , -4 3 , 4 , 4 4 , 5 , 7 0 , 0 , 0 0 , 0 , 0 0 , 1 , 1

of migraine and through 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, 26]. We expect therefore that any improvement in drug delivery will mainly impact the pain free response.

Oral delivery profiles are better characterised by the pharmacokinetic parameters absorption rate (Ka) and lag time, as compared to non-parametrical estimates of the peak concentration (Cmax) and the time of its occurrence (T max). To identify the relation between absorption rate and response rate, four physiologically relevant values of Ka were evaluated in our analysis. Two of these (1.28 h⁻¹and 2.56 h⁻¹) were larger than the absorption rate 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 [26]. Similarly, four values of lag time were evaluated, two larger than the lag time of the marketed oral formulation (0.48 h and 0.96 h) and one smaller (0.12 h). 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 overall variability in 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 comparing mean responses of different Ka or lag time values. This variability was expressed as 95% confidence intervals around the mean responses. Two mean responses were defined significantly different if their confidence intervals did not overlap. On the other hand, we incorporated pharmacokinetic variabil-

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ity in the evaluation of response by considering three different exposure levels (“low”,

“mean” and “high” exposure) for every Ka and lag time.

By increasing Ka, we observed a maximum gain in pain free response of 12% at 0.5 h post-dose after a 50 mg dose. This can be explained by the fact that at 0.5 h plasma concentrations are equivalent to the potency (EC50) value on the concentration effect curve. At this point response is most sensitive to changes in concentration. Though with increasing absorption rate responses initially increase, this may result in lower expo- sures at later time points with consequent reduction in response (Figure 5.4). In fact, the response of the reference formulation is significantly different from the alternative hypothetical formulations only up to two hours post-dose (Figure 5.6, bold segments). Our findings coincide with reported clinical data. In the case of the 2 h pain free response after a 100 mg dose of marketed sumatriptan, 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% [27].

Furthermore, our analysis revealed that decreasing lag time with respect to the reference value of 0.24 h is not as efficient as a change in Ka. A maximum gain of 5%

was predicted for the 0.12 h 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 of this parameter. However, the value for the reference formulation was based on an analysis of data from healthy volunteers. In migraine patients, absorption lag time may be prolonged by the presence of gastric stasis [28]. We cannot quantify whether additional changes in lag time can be achieved. Our analysis has been performed assuming that the concentration vs ef- fect relation is constant under all absorption conditions. At high absorption rates the concentration-effect relationship might vary since the earlier availability of drug at the site of action may affect central sensitisation and have repercussion on later stages of the attack.

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

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