1.1.3 Balanced Truncation
The balanced truncation is based on an observation from control theory
that the least observable and least controllable states have no
significant contribution to the input-output relationship of interest
[36]. Therefore, removing such states from the system results in a
reduced-order model that retains most of the input-output behaviour of
the full-order model, but, unfortunately, masks the mechanistic basis of
the model. Balanced truncation can be viewed as a semiparametric
model-order reduction method because it is a function of model parameter
although the solution it produces is empirical.
Balanced truncation is typically employed for simplification of linear
systems. Of note, Snowden et al. [29] used this approach for
reducing a general physiologically based pharmacokinetic (PBPK) model
from 16-state to a 5-state system while incurring less than 1% maximal
relative error in prediction of venous compartment concentration. A
generalisation of this approach to a nonlinear system, called empirical
balanced truncation, through numeric approximation of the transformation
process, has been proposed [37]. An application of this approach to
nonlinear systems biology type models has been recently published
[38]. An extension of this approach to a framework where parameters
of interest are preserved in the reduced model has also been proposed
[25]. These improvements to balanced truncation technique make it
highly applicable to QSP models although no such application has been
published yet.