# A theoretical optimal experiment design for accurate estimation of key parameters of a dynamic mechanistic model representing the effect of Asparagopsis taxiformis on rumen fermentation and methane production under in vitro continuous conditions

Rafael Muñoz-Tamayo, Tristan Senga Kiessé, Maguy Eugène, Paul Blondiaux

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Rafael Muñoz-Tamayo, Tristan Senga Kiessé, Maguy Eugène, Paul Blondiaux. A theoretical optimal experiment design for accurate estimation of key parameters of a dynamic mechanistic model representing the effect of Asparagopsis taxiformis on rumen fermentation and methane production under in vitro continuous conditions. 11. Workshop on Modelling Nutrient Digestion and Utilization in Farm Animals (Modnut 2025), Agroscope, Sep 2025, Engelberg, Switzerland. pp.456, 10.1016/j.anscip.2025.07.285. hal-05372609

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Submitted on 19 Nov 2025

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38. A theoretical optimal experiment design for accurate estimation of key parameters of a dynamic mechanistic model representing the effect of *Asparagopsis taxiformis* on rumen fermentation and methane production under *in vitro* continuous conditions

R. Muñoz-Tamayo<sup>a</sup>, T. Senga Kiessé<sup>b</sup>, M. Eugène<sup>c</sup>, P. Blondiaux<sup>a</sup>

Corresponding author: Rafael Muñoz-Tamayo. E-mail: rafael.munoz-tamayo@inrae.fr

**Introduction:** Reducing methane (CH₄) emissions from ruminants is a major target for the livestock sector. Synergy between *in vitro* studies and models can be useful to provide high quality data enabling to quantify the mode of action of anti-methanogenic additives and thus robust mitigation solutions. The objective of this work was to conduct a theoretical optimal experiment design (OED) to identify experimental conditions for attaining accurate estimates of key parameters of a model we previously developed representing the impact of the anti-methanogenic macroalgae *Asparagopsis taxiformis* on rumen fermentation and CH₄ production under *in vitro* continuous conditions (Blondiaux et al. 2024).

**Material and methods:** *A. taxiformis* contains the anti-methanogenic compound bromoform (we assumed a bromoform content in the macroalgae of 0.684 % in the DM). CH₄ inhibition results in hydrogen (H₂) accumulation. H₂ exerts thermodynamic control on the fermentation via the flux allocation towards volatile fatty acids production. We applied the OED to 5 model parameters related to the mode of action of *A. taxiformis*: *k*₁ (inhibitor bromoform constant) and *p*₁, *p*₂, *p*₃, *p*₄ (parameters of affine functions representing flux allocation factors). We assessed the parameter identifiability with GenSSI (Ligon et al. 2018) assuming that the measurements are the concentrations of acetate, butyrate, propionate and bromoform in the liquid phase, and CH₄, H₂, CO₂ in the gas phase. Then, we solved an OED problem for parameter estimation for a 24 h run allowing an accurate parameter estimation. For that, we used the D-optimality criterion that maximizes the determinant of the Fisher information matrix (FIM). The OED problem was set as minDet(FIM), with φₐ the design vector.

φₐ = [w<sub>br</sub>, t₁, t₂, ..t₁₀], with w<sub>br</sub> the bromoform content in the feed, tᵢ the sampling times (h). The FIM was calculated by symbolic manipulation in Matlab. The optimization was done using the Matlab function fminsearch (Nelder-Mead Simplex Method).

**Results and discussion:** The parameters are globally identifiable. The optimal sampling were [0; 3.6; 5.7; 7.8; 11.4; 13; 15.4; 19.3; 22.4; 24] and the optimal bromoform content was 0.0020 % DM. Table 1 shows the standard deviations (s.d.) of the parameters by the OED compared to a classical equidistant sampling (ES) with a w<sub>br</sub> of 0.0034 % DM. In average the s.d of the OED are 58 % of the s.d. with equidistant sampling.

<table><caption>Table 1 Ratio of the s.d. of the parameter estimates from the OED to the s.d. from an equidistant sampling (ES).</caption><thead><tr><th></th><th>k<sub>1</sub></th><th>p<sub>1</sub></th><th>p<sub>2</sub></th><th>p<sub>3</sub></th><th>p<sub>4</sub></th></tr></thead><tbody><tr><td>100-s.d OED/s.d. ES</td><td>102</td><td>33</td><td>60</td><td>35</td><td>61</td></tr></tbody></table>

**Conclusion and implications:** We showed the benefits of OED for accurate parameter estimates. Applying OED can be instrumental for conducting experiments whose data will allow the construction of robust rumen fermentation models for helping the design of CH₄ mitigation strategies.

**Financial support:** R. Muñoz-Tamayo acknowledges funding from the ANR project H2Rumen (ANR-24-CE20-7802).

**References:**

Blondiaux P, Kiessé TS, Eugène M, Muñoz-Tamayo R. 2024. Dynamic sensitivity analysis of a mathematical model describing the effect of the macroalgae *Asparagopsis taxiformis* on rumen fermentation and methane production under *in vitro* continuous conditions. Biorxiv, https://doi.org/10.1101/2024.06.19.599712.

Ligon, T.S., Fröhlich, F., Chiş, O.T., Banga, J.R., Balsa-Canto, E., Hasenauer, J., 2018. GenSSI 2.0: multi-experiment structural identifiability analysis of SBML models. Bioinformatics 34, 1421–1423. https://doi.org/10.1093/bioinformatics/btx735.

doi: 10.1016/j.anscip.2025.07.285

39. Modelling collective manure management scenario and their environmental impacts

A. Cadero<sup>a,b</sup>, F. Garcia-Launay<sup>a</sup>, P. Levasseur<sup>b</sup>, V. Blazy<sup>c</sup>, S. Foray<sup>d</sup>, P. Thiriet<sup>e</sup>, S. Espagnol<sup>b</sup>

<footnote><sup>a</sup>Université Paris-Saclay, INRAE, AgroParisTech, UMR Modélisation Systémique Appliquée aux Ruminants, 91120 Palaiseau, France</footnote>

<footnote><sup>b</sup>INRAE, UMR SAS, Institut Agro, 35000 Rennes, France</footnote>

<footnote><sup>c</sup>Université Clermont Auvergne, INRAE, VetAgro Sup, UMR Herbivores, Saint-Genes-Champanelle, France</footnote>

<footnote><sup>a</sup>UMR PEGASE, INRAE-Institut Agro, 16 le clos, 35590 Saint-Gilles, France</footnote>

<footnote><sup>b</sup>Ifip-Institut du Porc, 9 bd du Trieux, 35740 Pacé, France</footnote>

<footnote><sup>c</sup>ITAVI, rue Maurice Le Lannou, 35000 Rennes, France</footnote>

<footnote><sup>d</sup>IDELE, Monvoisin, 35650 Le Rheu, France</footnote>

<footnote><sup>e</sup>UR OPAALE, INRAE, 17 avenue de Cucillé, 35044 Rennes, France</footnote>

<footnote>* Corresponding author: Alice Cadero. E-mail: alicecadero@inrae.fr</footnote>