Hugo Maas, Oscar Della Pasqua, Meindert Danhof
LACDR, Leiden University, Division of Pharmacology
Triptans (such as sumatriptan and naratriptan) are efficacious and specific medications in the treatment of migraine. Yet, assessing clear pharmacokinetic-pharmacodynamic (PK-PD) relations for these drugs is difficult. In most clinical studies the actions of triptans in the trigeminal system are measured indirectly using pain-rating scales. As a consequence , sources of variability stemming from the multiple levels of pain control are added to the original trigeminal signal. Furthermore, little is known about the kinetics of pathophysiological mechanisms involved in migraine, which complicates the design of predictive mechanism-based models.
In principle a PK-PD model for triptans should be based on a set of physiologically meaningful parameters. The facts that little information on the disease is available and that the endpoint is a categorical variable, impose that the model be stochastic. A class of structural models that provide these features are the hidden Markov models1.
To test the hidden Markov model concept, a model was developed to describe the course of a single migraine attack. It consists of two layers: i) a hidden layer representing the (unobserved) states of trigeminal activity and ii) an observational layer that transforms trigeminal activity into a headache score. The connectivity between the unobserved states was assumed to be unidirectional, in order of decreasing trigeminal activity. The parameters in this part of the model include the elements of the intensity matrix, which can be considered rate constants of the trigeminal activation process. The headache scores returned by the observational layer are multinomially distributed conditional on the unobserved state. The parameters in this layer are the elements of the emission matrix, reflecting the influence of pain control processes on the trigeminal pain signal. The model was applied to estimate parameters from pain score data obtained from clinical trials with sumatriptan.
In this analysis the transitions in the hidden layer are functions of plasma drug concentration. Demographic variables such as age and sex were incorporated into both layers to explain variability in pain response.
1
L. Rabiner. A tutorial on hidden Markov models. Proc. IEEE, 77:257–286, 1989.Reference: PAGE 12 (2003) Abstr 367 [www.page-meeting.org/?abstract=367]
Poster: poster