Claudia Stötzel and Marcus Weber and Susanna Röblitz
Zuse Institute Berlin
Objectives: For the simulation of biological models, the identification of unknown parameter values such as growth and clearance rates of the involved substances is crucial. For a model of the female menstrual cycle, we use Bayesian methods to recover the joint probability distributions of the free parameters. We analyse the sampled marginal distributions and detect parameter regions which lead to pathological situations.
Methods: For a previously developed mechanistic model of the human menstrual cycle [1], which consists of 33 highly nonlinear ODEs and 113 parameters, we sample the joint posterior distribution of 82 free parameters. For this, a Metropolis-Hastings algorithm to generate a Markov chain that walks through the parameter space is implemented in Python. To account for the positivity of the parameters, a log-normal distribution is chosen for the transition probabilities. As the solution of the model has to be cyclic, only periodic solutions are accepted and, in every step, the data is shifted to match the periods. For the calculation of the likelihood, data were available for 40 individuals in courtesy of Dorothea Wunder, CHUV, Lausanne, and for 12 individuals from a previous collaboration with Pfizer [1]. The sampled marginal parameter distributions are divided into intervals for which the transition probabilities are calculated and analysed.
Results: Several bimodal marginal parameter distributions are detected, which give a hint to a clustering of important parameter values. In particular, we found a set of parameter values that leads to the simulation of the polycystic ovary syndrome (PCOS).
Conclusions: The clustering of the marginal parameter distributions is a suitable approach to explore the parameter space and detect new dynamical characteristics of a given model. Our analysis is promising to lead to even more insights about unexplored simulation possibilities with an ODE model of biological processes.
References:
[1] S. Röblitz, C. Stötzel, P. Deuflhard, H. M. Jones, D. O. Azulay, P. van der Graaf, and S. W. Martin. A mathematical model of the human menstrual cycle for the administration of GnRH analogues. Journal of Theoretical Biology, 321:8–27, 2012.
Reference: PAGE 24 (2015) Abstr 3394 [www.page-meeting.org/?abstract=3394]
Poster: Methodology - Estimation Methods