1.1.1 Lumping
Lumping is a general concept that we use in our daily lives to simplify the description of objects. For instance, we use the collective term “fruit” to describe the sweet and fleshy seed-containing products of plants. This semantic lumping is useful because many fruits have common properties so can be treated as a single concept (a lump). Similarly, in QSP models, some nodes can be grouped (lumped) into a single node to produce a simpler form of the model which can be more easily solved. This reduces the number of parameters that need to be experimentally determined [31].
The concept of lumping is relatively simple, conceptually, as all you need to do is to lump together every possible combination of nodes and find the simplest model that retains the desired prediction characteristics of the lumped model when compared to the full-order model. However, the number of possible combinations grows very fast with the size of the model leading to an unfeasibly long list of combinations to be tested. To overcome this issue, Dokoumetzidis et al. [32] proposed a greedy search approach to find the optimal lumping scheme. The utility of the approach was demonstrated by reducing a 62-dimensional model of NF-κB signalling pathway to a 13-dimensional model with acceptable accuracy.
Hasegawa and Duffull proposed an automatable approach to lumping nonlinear QSP models [18] by first linearising the QSP model then lumping using standard techniques. Using this approach, a 28-state bone biology model was reduced to an 8-state model that retained sufficient mechanistic detail to be able to extrapolate to new data for two examples (denosumab and alendronate). In the former case, the model was able to predict long-term responses from short to medium-term data [18] while in the latter, the reduced model for denosumab was reused successfully for alendronate without reference to the original QSP model and without further development of the reduced model [19]. Another approach was applied by Gulati et al. [22] who used an arbitrary series of lumping steps to search through for the optimal lumping scheme. In this approach a 62-state QSP model of the coagulation system was lumped to a 5-state model that was used as the basis for estimating the effect of snake-bite on fibrinogen kinetics.