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.