A framework for considering model-order reduction methods
A wide range of model-order reduction methods have been described [18,21,22,24-27] each of which has its own strengths and weaknesses. An ideal model-order reduction method should have the following characteristics:
  1. System agnostic, i.e. universally applicable to different biological systems and model use,
  2. Automatable, i.e. does not require user input,
  3. Mechanistically relevant, i.e. the simplified model contains the necessary features that enable its use for a wide variety of settings
  4. Accurate, i.e. able to replicate important data predictions,
  5. Computational ease, i.e. identifiable and be of little computational burden,
  6. Preserve extrapolation ability of the full-order model,
  7. Requires no experimental data to derive the reduced-order model, and
  8. Able to be used for parameter estimation.
However, an ideal method does not exist, therefore it is necessary for the investigator to select the method. Understanding how the methods relate to each other and what they contribute is therefore of particular importance.
There are several ways that methods of model-order reduction can be categorised. Snowden et al. [28] in their review adopted four categories to summarise these techniques based on their internal mathematical methods, namely, time-scale exploitation, optimisation and sensitivity analysis, lumping, and singular value decomposition methods. We contend that, the utility of model-order reduction techniques lies not in their internal mathematical properties but in their use-effectiveness of simplifying various problems. In this review, we have adopted a framework that allows a natural categorisation of methods based on their utility. The framework is outlined in Figure 2.
In the proposed framework, we categorise model reduction methods into parametric and nonparametric methods. Parametric methods aim to simplify the structure of the model, which is typically achieved by either reducing the number of nodes (species of interest and compartments) or edges (reactions, fluxes and interactions). Nonparametric methods, on the other hand, simplify the input-output relationship through construction of an empirical (surrogate) model that has a simpler structure but can emulate the behaviour of the full-order model. There are, of course, hybrid methods that use both approaches and approximate some components of the system with a black box while using mechanistic simplification methods on the structure of other components [29].
All methods provide a simplified relationship between the model inputs (i.e. drug, dose, dose-time) with the outputs (i.e. the response variable of interest) that can then be manipulated easily to describe and predict new data.