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.