(181b) Model-Based Design of Biokinetic Experiments for Foliar Uptake of Pesticides

The global population is expected to increase further and peak around 10 billion people towards the end of the 21^st century (United Nations, 2024). With the increasing population food security issues will become even more serious (Roy et al., 2024) and must be addressed, considering the sustainability of the solutions while satisfying the food demand. In this direction, crop protection science is important to preserve the agricultural resources we have from competitive agents such as weeds and pests, but it must be ensured that the novel solutions are safe for the environment and aligned with sustainable agricultural practices (Umetsu and Shirai, 2020).

In fields applications, one of the most common techniques to deliver pesticides to crops is by spraying formulated products on their foliage. The whole chain of processes that bring the AI molecule from the tank mix to the target sites, i.e. biological macromolecules with essential physiological functions that interact with the AI at cellular level (Zhang et al., 2025), impacts the overall efficacy of the crop treatment. This study focuses on the process of AI uptake from the droplet deposited on the leaf surface to the molecule being metabolized by the crop, i.e. the foliar uptake process (Franke, 1967).

Similarly to the pharmaceutical sector, also in the crop protection sector tens of thousands of new molecules are developed by companies every year, but only a very small fraction of these molecules shows significant activity towards the biological targets. Furthermore, conducting experiments on crops and plants is expensive and extremely time consuming. Therefore, promising molecules, if tested with a sub-optimal formulation that prevents them to maximize their performance, could potentially be discarded in early research stages in favour of other molecules due to the limited resources to test all the new AIs under development. This situation creates a significant bottleneck in the early stages of development of new biocide solutions.

This issues suggest that introducing computational tools and mathematical models as part of this research process could be beneficial from different points of view: i) to better understand the interaction between formulated AI and crop, ii) to predict which molecules are more promising and adequately allocate the required experimental resources, and iii) to optimize the experimental procedure so that the maximum information is extracted under the constraint of limited resources and time.

To achieve these benefits, mathematical models have to be developed and validated, considering the confidence in model predictions. In this study, foliar uptake modelling is approached adopting a systematic procedure based on the framework proposed by Franceschini and Macchietto (2008). The key steps in this procedure are:

1. Formulation of candidate models and identifiability analysis.
2. Characterization of the variability in data.
3. Model-based design of experiments.
4. Precise parameter estimation.
5. Model validation.

The first step has been addressed by the authors in previous studies where different type of models, i.e. compartmental (Sangoi et al., 2024a) and diffusion-based models (Sangoi et al., 2024b) have been proposed and tested for parameter identifiability.

Step 2, the characterization of uncertainty in data, is crucial prior the application of MBDoE techniques (step 3), in order to guarantee that the quantified expected information for the new experiments is reliable. In the case of foliar uptake, replicates of biokinetic experiments are obtained from different leaves or plants, since the measurements are destructive, and this introduces biological variability (Badrick, 2021) in the observed variance from the samples along with the measurement error. This aspect must be considered in the application of MBDoE for foliar uptake experiments.

Model-based design of experiments techniques (Franceschini and Macchietto, 2008) exploit the knowledge that can be extracted from the model to guide the experimental design, differently from statistical DoE techniques such as full-factorial and Latin-hypercube designs which aim to cover the experimental space as widely as possible (Pukelsheim, 2006). MBDoE can be used with different purposes, i.e. for model discrimination (Schwaab et al., 2008), for improving parameter precision or reducing the uncertainty on model predictions (Cenci et al., 2023), or a combination of the above. In all cases, the model is involved in the calculation of the objective function for the experimental design optimization, with different mathematical expressions depending on the problem to target.

In the case of foliar uptake, the biokinetic experiments are conducted by spraying the product on the leaves (defining time ) and then at each sampling time two mass measurements are collected: the mass of AI on the leaf surface and the mass of AI inside the leaf, extracted by macerating the leaf. In an experimental campaign, multiple sampling times are considered to observe the dynamic profile of uptake and metabolism, and replicates at the same sampling time are performed to obtain a confidence interval in the observed experimental values.

The optimal allocation of the experimental resources and of sampling times is approached in this study with MBDoE, to obtain the most informative data that can lead to more reliable models while saving experimental resources. Different MBDoE approaches are compared to optimize the design of biokinetic experiments for foliar uptake and the relative advantages and disadvantages of different MBDoE approaches are compared and discussed. Results show how MBDoE can be used to guide the practical application of mathematical models combined with biological experiments for the discovery of new biocides, minimizing time and resources for model development.

References

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