A theoretical optimal experiment for accurate parameter estimation of a dynamic rumen model representing the Asparagopsis taxiformis effect on in vitro methane production

Reducing methane (CH4) emissions from ruminants is a major target for the livestock sector. Synergy between in vitro studies and mathematical models can be useful to provide high quality data enabling to quantify the mode of action of anti-methanogenic additives and thus design robust mitigation solutions. The objective of this work was to conduct a theoretical optimal experiment design (OED) to determining optimal experimental conditions allowing an accurate estimation of key parameters of a model we previously developed representing the impact of the anti-methanogenic macroalgae Asparagopsis taxiformis on rumen fermentation and CH4 under in vitro continuous conditions. A. taxiformis contains the anti-methanogenic compound bromoform which inhibits directly the growth rate of methanogens. 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 framework to 5 model parameters related to the mode of action of A. taxiformis: (inhibitor bromoform constant) and (parameters of affine functions representing flux allocation factors). After conducting a structural parameter identifiability analysis to guarantee that the parameter identification problem was well-posed, we set the OED problem for parameter estimation using the D-optimality criterion which maximizes the determinant of the Fisher information matrix () using as decision variables the bromoform content in the feed and five sampling times for a run duration of 24 h. The OED problem was solved for four feed intake patterns. The accuracy of the parameter estimates was determined by the calculation of the standard deviations (s.d.) and compared with the s.d. obtained with a classical equidistant sampling protocol. The resulting optimal solutions were shown to be specific to each feed distribution pattern. The gain in accuracy of the OED protocol with respect to the equidistant sampling depended on the pattern of feed intake. For the highest gain, the s.d. by the OED protocol were in average 57% of the s.d. of the equidistant sampling protocol. For the lowest gain, the s.d. of the OED protocol were in average 92% of the s.d. of the equidistant sampling protocol. These results demonstrate the potential of the OED approach for obtaining accurate parameter estimates, and highlight the importance of selecting an optimal supply of feed additives. Using the OED approach can be instrumental for conducting experiments that produce data for building robust rumen fermentation dynamic models that can help the design of CH4 mitigation strategies.