Automated QSP model order reduction combining multiple state-level reduction approaches

Johannes Tillil (1,2), Jane Knöchel (2,3), Charlotte Kloft (4), and Wilhelm Huisinga (2)

(1) PharMetrX Graduate Research Training Program: Pharmacometrics & Computational Disease Modelling, Freie Universität Berlin and University of Potsdam, Germany, (2) Institute of Mathematics, University of Potsdam, Germany, (3) Current Address: AstraZeneca R&D, Mölndal, Sweden, (4) Institute of Pharmacy, Freie Universität Berlin, Germany

Objectives: Quantitative systems pharmacology (QSP) models are useful tools for drug target identification and extrapolation. However, their large size can lead to prohibitive computational cost and can complicate interpreting the model dynamics. When analyzing specific input-response relationships within a QSP model, not all states may significantly contribute to the dynamics of interest. Model order reduction methods can remove such unimportant states [1]. They can reduce the computational cost of performing analyses as well as reduce complexity by removing states and parameters from the model.

However, there is not a single best reduction method for all QSP models. By combining different reduction approaches, we could obtain a more generally applicable procedure. Previously, an iterative method has been developed that can automatically either neglect states or set them to a constant value [2]. We aimed to improve upon this work by systematically evaluating more reductions in the search of a reduced model and by including more state-level reduction approaches, motivated by a recent publication on index analysis [3].

Methods: We implemented model order reduction in an iterative framework. Starting from the full model, once per iteration all states are tentatively (i) neglected (NEG), (ii) set to a constant value equal to either their initial concentration (ENV) or our novel observability-weighted environmental state concentration (OENV) or (iii) are expressed via the quasi-steady-state approximation (QSSA). One particular reduction to apply to the model is then chosen with a greedy approach based on an objective function which considers the relative error (RE) of the model output, as well as the RE of all remaining states. This ensures that all remaining model components are well approximated and can still be interpreted as the same biological entity they represented in the full model.

Results: The number of dynamic states n and RE of the reduced models of EGF signaling are, using NEG+ENV: n = 55, RE = 2.4%, NEG+ENV+QSSA: n = 34, RE = 2.2% and NEG+ENV+QSSA+OENV: n = 15, RE = 2.4%. The three reduced blood coagulation models contain n = 4 dynamic states and have a RE of 0.2%. The procedure automatically chose to not include any QSSAs in the reduction of the blood coagulation model. Both QSP models could be substantially reduced while achieving only a small RE on the output.

During reduction of the model of EGF signaling we observed the intriguing feature that the RE of approximating the full QSP model can also decrease instead of increase when a state is reduced. To exploit this, we performed model order reduction until no dynamic state was left. This approach considerably lowered the size of the reduced models returned by our procedure.

Conclusions: The iterative model order reduction procedure yields small-scale mechanistic models with significantly reduced complexity that retain interpretability of all remaining model components. The addition of the QSSA and the novel environmental states improves the effectiveness of the reduction. Variability and further simplification by parameter reduction can be included in the procedure similar to [6].

References:

Reference: PAGE 32 (2024) Abstr 11225 [www.page-meeting.org/?abstract=11225]

Poster: Drug/Disease Modelling - Other Topics

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