Identifiability of large-scale non-linear dynamic network models applied to the ADM1-case study

ASAS-NANP symposium: Mathematical Modeling in Animal Nutrition: The power of identifiability analysis for dynamic modeling in animal science:a practitioner approach

Constructing dynamic mathematical models of biological systems requires estimating unknown parameters from available experimental data, usually using a statistical fitting procedure. This procedure is usually called parameter identification, parameter estimation, model fitting, or model calibration. In animal science, parameter identification is often performed without analytic considerations on the possibility of determining unique values of the model parameters. These analytical studies are related to the mathematical property of structural identifiability, which refers to the theoretical ability to recover unique values of the model parameters from the measures defined in an experimental setup and use the model structure as the sole basis. The structural identifiability analysis is a powerful tool for model construction because it informs whether the parameter identification problem is well-posed (i.e., the problem has a unique solution). Structural identifiability analysis is helpful to determine which actions (e.g., model reparameterization, choice of new data measurements, and change of the model structure) are needed to render the model parameters identifiable (when possible). The mathematical technicalities associated with structural identifiability analysis are very sophisticated. However, the development of dedicated, freely available software tools enables the application of identifiability analysis without needing to be an expert in mathematics and computer programming. We refer to such a non-expert user as a practitioner for hands-on purposes. However, a practitioner should be familiar with the model construction and software implementation process. In this paper, we propose to adopt a practitioner approach that takes advantage of available software tools to integrate identifiability analysis in the modeling practice in the animal science field. The application of structural identifiability implies switching our regard of the parameter identification problem as a downstream process (after data collection) to an upstream process (before data collection) where experiment design is applied to guarantee identifiability. This upstream approach will substantially improve the workflow of model construction toward robust and valuable models in animal science. Illustrative examples with different levels of complexity support our work. The source codes of the examples were provided for learning purposes and to promote open science practices.

Assessing practical identifiability during calibration and cross-validation of a structured model for high-solids anaerobic digestion

High-solids anaerobic digestion (HS-AD) of the organic fraction of municipal solid waste (OFMSW) is operated at a total solid (TS) content ≥ 10% to enhance the waste treatment economy, though it might be associated to free ammonia (NH₃) inhibition. This study aimed to calibrate and cross-validate a HS-AD model for homogenized reactors in order to assess the effects of high NH₃ levels in HS-AD of OFMSW, but also to evaluate the suitability of the reversible non-competitive inhibition function to reproduce the effect of NH₃ on the main acetogenic and methanogenic populations. The practical identifiability of structural/biochemical parameters (i.e. 35) and initial conditions (i.e. 32) was evaluated using batch experiments at different TS and/or inoculum-to-substrate ratios. Variance-based global sensitivity analysis and approximate Bayesian computation were used for parameter optimization. The experimental data in this study permitted to estimate up to 8 biochemical parameters, whereas the rest of parameters and biomass contents were poorly identifiable. The study also showed the relatively high levels of NH₃ (i.e. up to 2.3 g N/L) and ionic strength (i.e. up to 0.9 M) when increasing TS in HS-AD of OFMSW. However, the NH₃ non-competitive function was unable to capture the acetogenic/methanogenic inhibition. Therefore, the calibration emphasized the need for target-oriented experimental data to enhance the practical identifiability and the predictive capabilities of structured HS-AD models, but also the need for further testing the NH₃ inhibition function used in these simulations.