Automated proper lumping for the simplification of linear systems

Background
Complex system models may need to be simplified into simpler structures for many practical applications. Proper lumping is a simplification method that merges the original states into fewer pseudo states to produce a reduced system [1]. Recently a proper lumping technique has been used for the simplification of a large-scale systems pharmacological model [2].
Aim
To develop an automated process for model simplification using proper lumping technique.
Materials & Methods
An automated proper lumping process was implemented in MATLAB®. The user is required to provide the micro-rate constant matrix and the values of the micro-rate constants. The acceptance criterion is defined as the simplest structure that has a maximum loss of a 20% absolute relative difference in the prediction of the area under time-concentration curve (AUC) between the original and lumped models. A non-adaptive random search algorithm is currently implemented to search the combinations of lumped models. While this method is effective it is very inefficient for large models which constitute large combinatorial problems. An adaptive stochastic search algorithm is described as a probabilistic algorithm that converges asymptotically to the optimal solution under a pre-defined penalty function.
The automated lumping process is illustrated for a simple 9-state linear pharmacokinetic (PK) model of methotrexate [3].
Results
With the non-adaptive search algorithm, the original methotrexate PK model was simplified into 3-state model with 9.3% absolute relative difference in the AUC for the output state. The adaptive stochastic search algorithm is under development for simplifying more complex model structure as in physiologically-based PK models.
Conclusions
Methods for automatic model simplification represent large-scale combinatorial search problems. It is expected that these methods will have significant potential benefits for those using multi-scale models.
References
1. Dokoumetzidis A and Aarons L. IET Syst Biol. 2009;3(1): 40-51.
2. Gulati A et al. CPT Pharmacometrics Syst Pharmacol. 2014;3: e90.
3. Korell J et al. Clin Pharmacokinet. 2013;52(6): 475-485.

Shan Pan

  • University of Otago, School of Pharmacy