**Lumping of compartments**

Aris Dokoumetzidis

University of Athens

Interest in simplification of large mechanistic mathematical models of biological systems which are usually described by differential equations, has increased in recent years as Systems Biology is growing. Often model reduction techniques are borrowed from Petroleum Science where simplification of particularly large models of thousands of chemical reactions is widely used. In the field of Pharmacokinetics, simplification of large models has been considered mainly for Whole Body Physiologically Based Models (PBPK), while the potential of bridging the gap between the bottom-up, knowledge driven, systems biology models and the top-down, data driven models of empirical PK-PD, sounds intriguing.

The main approaches for model simplification are elimination of states and reactions (or flows) and lumping of states or compartments. While lumping can be any linear or indeed nonlinear transformation of the states of the original model to new, fewer in number states, a special case called proper lumping, allows a clear physical interpretation of the reduced model since each state of the original model contributes to a single state of the reduced model. The main question of any lumping algorithm is to determine exactly which states are to be grouped together. Also one of the main problems of model reduction is that it produces models which are valid locally in the parameter space and therefore robustness of a reduced model is crucial.

In this presentation an introduction on lumping will be discussed with emphasis on pharmacokinetics with relevant examples.