Respiration of bulky plant organs such as roots, tubers, stems, seeds, and fruit depends very much on oxygen (O 2 ) availability and often follows a Michaelis-Menten-like response. A multiscale model is presented to calculate gas exchange in plants using the microscale geometry of the tissue, or vice versa, local concentrations in the cells from macroscopic gas concentration profiles. This approach provides a computationally feasible and accurate analysis of cell metabolism in any plant organ during hypoxia and anoxia. The predicted O 2 and carbon dioxide (CO 2 ) partial pressure profiles compared very well with experimental data, thereby validating the multiscale model. The important microscale geometrical features are the shape, size, and three-dimensional connectivity of cells and air spaces. It was demonstrated that the gas-exchange properties of the cell wall and cell membrane have little effect on the cellular gas exchange of apple (Malus 3 domestica) parenchyma tissue. The analysis clearly confirmed that cells are an additional route for CO 2 transport, while for O 2 the intercellular spaces are the main diffusion route. The simulation results also showed that the local gas concentration gradients were steeper in the cells than in the surrounding air spaces. Therefore, to analyze the cellular metabolism under hypoxic and anoxic conditions, the microscale model is required to calculate the correct intracellular concentrations. Understanding the O 2 response of plants and plant organs thus not only requires knowledge of external conditions, dimensions, gas-exchange properties of the tissues, and cellular respiration kinetics but also of microstructure.

We present a combined three-dimensional (3-D) model of light propagation, CO2 diffusion and photosynthesis in tomato (Solanum lycopersicum L.) leaves. The model incorporates a geometrical representation of the actual leaf microstructure that we obtained with synchrotron radiation X-ray laminography, and was evaluated using measurements of gas exchange and leaf optical properties. The combination of the 3-D microstructure of leaf tissue and chloroplast movement induced by changes in light intensity affects the simulated CO2 transport within the leaf. The model predicts extensive reassimilation of CO2 produced by respiration and photorespiration. Simulations also suggest that carbonic anhydrase could enhance photosynthesis at low CO2 levels but had little impact on photosynthesis at high CO2 levels. The model confirms that scaling of photosynthetic capacity with absorbed light would improve efficiency of CO2 fixation in the leaf, especially at low light intensity.

Since many years food engineers have attempted to describe physical phenomena such as heat and mass 31 transfer that occur in food during unit operations by means of mathematical models. Foods are hierarchi-32 cally structured and have features that extend from the molecular scale to the food plant scale. In order to 33 reduce computational complexity, food features at the fine scale are usually not modeled explicitly but 34 incorporated through averaging procedures into models that operate at the coarse scale. As a conse-35 quence, detailed insight into the processes at the microscale is lost, and the coarse scale model parame-36 ters are apparent rather than physical parameters. As it is impractical to measure these parameters for 37 the large number of foods that exist, the use of advanced mathematical models in the food industry is 38 still limited. A new modeling paradigm -multiscale modeling -has appeared that may alleviate these 39 problems. Multiscale models are essentially a hierarchy of sub-models which describe the material 40 behavior at different spatial scales in such a way that the sub-models are interconnected. In this article 41 we will introduce the underlying physical and computational concepts. We will give an overview of 42 applications of multiscale modeling in food engineering, and discuss future prospects. 43

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