**2. Problem formulation**

**i.** *The presence of chemical compounds in the environment and biota* is the subject of global interest with the general aim to ensure that their impact on humans, other living organisms, and the environment is minimized. Chemicals that once enter the environment can persist or support different types of transformations resulting in new transformation products. Based on the characteristics of transformation products, these transformation processes could be either of benefit (attenuation processes) or be hazardous (when the resultant transformation products possess more hazardous characteristics than the "parent" compound).

**1. Introduction**

198 Numerical Simulations in Engineering and Science

chemical use.

**2. Problem formulation**

Thousands of chemicals are used in industry, agriculture, pharmacy, commerce, and daily life. With that, a large number of chemical compounds enter the environment. Often these are considered with potential harmful effects on environmental media quality and biota safety. Thus, the understanding of them is crucial both for a better management of their use and for the better protection of the environment and living organisms. Monitoring these chemical compounds frequently is time-consuming and requires large financial efforts; one of the most cost-effective as well as time-efficient methods of evaluating their behavior in the environ-

Experimental data and models for chemical compounds' fate and kinetics in living organisms play a crucial role for assessing the potential human and ecological risks associated with

Plants are receptor organisms and could be either direct or indirect vectors for chemical exposure to all other organisms [1]. In the first instance, the generated experimental data considering chemical concentrations in different media of the environment and biota are necessary to improve our understanding on plant-chemical-environment interactions. These, in turn, admit and bring forward the development of better scientific knowledge as well as conceptual and predictive models on chemical partition, fate, and uptake [2]. The strong interconnections between experimental data and model development are continuous and a long-term updated process which is needed to advance our ability to provide reliable quality information that can be used in various environmental protection contexts and regulatory risk assessments [1]. At this moment there are no standard protocols both for chemical compounds' bioaccumulation data generation and for data use for prediction through numerical methods [1, 3]. For the reliable modeling of plant-chemical-environment interactions with the major goal to predict chemical compounds' fates and kinetic in living organisms, it is necessary to understand and keep into account all process, phenomena, and characteristics of both chemicals and receptors (living organisms and the environment) and the interconnected process between them. Inconsistent data collection, inaccurate generation of them, or reporting them with gaps will provide improper and less useful information for their application in assessment and numerical model development. This chapter is about to find optimal numerical modeling ways considering chemical compounds' fate and kinetics in a living organism, specifically plants. The aim of this study was to propose a numerical procedure which estimates the highest accumulation rate of a chemical

compound of interest for a growing living organism and to validate the procedure.

**i.** *The presence of chemical compounds in the environment and biota* is the subject of global interest with the general aim to ensure that their impact on humans, other living organisms, and the environment is minimized. Chemicals that once enter the environment can persist or support different types of transformations resulting in new transformation products. Based

ment and living organisms could be the use of predictive numerical models.

**ii.** *Chemical compounds' transformation in the environment:* Based on chemical compounds' specific physicochemical properties as well of biogeochemical and physicochemical characteristics of the media in which they are discharged (soil, water, air), these chemicals can be distributed across different environmental compartments (soil, surface and/or underground water , air, sediments, etc.) and biota [4]. In almost all cases their accumulation in environmental or biota compartments is characterized by continuous dynamic processes such as volatilization, degradation, precipitation, sorption, and so on, processes that often have the potential to end up in the formation of new chemical compounds called as transformation products of the initial chemical compound (**Figure 1**). Often these compounds could enter in new reaction processes and for other new end products. A schematic diagram of principal processes that could take place in both environment and biota and their interconnection with the "initial" chemical compounds and "resultant" transformation products is presented in **Figure 1**.

Challenges considering potential transformation products are given by their physicochemical properties that in several cases could make them more harmful against environment quality or biota safety than the initial chemical compound. Both processes as well as the resultant transformation products' formation are directly dependent on the environmental conditions as well properties of chemicals.

**Figure 1.** A schematic presentation of the main processes involved in chemical compounds and corresponding potential transformation of products' fate between different environmental compartments and biota.

**i.** *Chemical compounds' uptake by plants*: Chemicals' uptake by plant organisms is a system of complex and multi-step processes. These processes could be classified firstly as chemical uptake and transportation between different anatomical compartments (e.g., root to any other anatomical compartment) and secondly as chemical uptake from different environmental compartments (route of exposure) and plant anatomical compartments (particle deposition, vapor uptake from the atmosphere, and so on). The amplitude of these processes is determined by physicochemical properties of the chemical that is under uptake [5]. Current literature presents clear-cut evidence that the availability of most organic chemical compounds is governed on the one hand by their lipophilicity and on the other hand depends on the organic matter (OM) content of the soil under consideration [6]. Some compounds form "bound" residues with organic matter (OM) or humus particles in the soil. Besides, the nature and rooting pattern of the vegetation will have greater influence on the solubility of chemicals. Exuding up to 25% of the net carbon fixed during photosynthesis into the rhizosphere, plants modify given soil-chemical interactions in multiple ways. Secondary plant products (phenolic) and soil bioactive compounds (carbohydrates, organic acids, etc.) could also impact soil micro-biodiversity that could influence in a positive way transformation of organic pollutants to reactive metabolites [7]. For example, it has been demonstrated that isoproturon is metabolized to available plant and reactive compounds in rhizosphere soil [8], while the bacterial conversion of arochlors to reactive metabolites has been one of the early results of bioremediation studies [9].

those often found in the rhizosphere in significant amounts [13, 14]. Also, lipophilic organic chemicals possess a greater tendency to partition into plant roots than hydrophilic chemicals. Although chemicals properties are important predictors of the uptake potential, the physiology and composition of the plant root itself is also a significant influence, with differences in the uptake potential explained by the varying types and amounts of lipids in root cells [15]. Uptake from the external media is often expressed as a root concentration factor (RCF), which is the ratio of chemical concentration in the root to the concentration found in external media [13, 16]. *Transfer from roots to other anatomical compartments of plants*: The major factor that illustrates the amount of a chemical compound that was transferred from the plant root part to other anatomical compartments is the transpiration stream concentration factor (TSCF) which is the ratio of chemical concentration in transpiration to the concentration found in the external part. TSCF could be predicted from knowledge of the chemical compound lipophilicity, with maximum uptake, a *logKOW* about 1 [17]. Once the chemical is transported to the stem, plant water and solutes take it and continue to transport these chemicals to the rest of the anatomi-

Numerical Modeling of Chemical Compounds' Fate and Kinetics in Living Organisms: An Inverse…

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*Vapor or gas uptake from ambient air*: Another exposure route with chemicals in case of plant materials could be the ambient air that contains a large number of contaminants. This exposure route is governed by gaseous exchange and facilitates the transport and uptake of chemicals that are volatiles and which are more easily partitioned in air than in water. This has been shown to be the main uptake pathway in the above-ground plant parts for a variety of chemical compounds (e.g. PCBs, tetra- and hexa-chlorinated PCDD/Fs) [19]. Previous studies have reported a good correlation between shoot uptake and chemical properties of compounds (KOW, Henry's Law constant, octanol-air partition coefficient, etc.). In studies presented by [20], it was evidenced that gaseous uptake is the primary pathway for chemicals with an

*Particulate deposition on plant surfaces*: Pesticides as well as other chemical contaminants are bound to soil particles which may be transported by wind and/or rain and deposited on the above-ground anatomical compartments of plants. Studies presented by [5, 21], evidenced that dry deposition onto the leaf of suspended particles that contain PCCD/Fs is the major route of uptake due to PCCD/Fs permeation through the cuticle. Similarly, in their studies, wet deposition was shown which could also be the dominant deposition mechanism for

To date, a number of mathematical models have been developed to facilitate the exposure assessment of chemical contaminants, with important results in the modeling of pollutants' multimedia fate and the modeling of pollutants' linkage with transformation products, espe-

The properties of wild growing mushrooms make them valuable resources both in culinary practices and in pharmaceutical practices. They are recognized as healthy food with low

[5, 21].

cal compartments through vascular systems and cell tissues [18].

octanol-air partition coefficient (logKOA) less than 11 [20].

organic chemicals with Henry's Law constant of less than 1 × 10<sup>−</sup><sup>6</sup>

cially in water environmental compartments [4].

**4. Case study presentation**

**ii.** Probably, one of the most effective ways to study chemical behavior and fate is to *use mathematical fate models*. Mechanistic environmental models use mathematical equations which describe the parameters of an environment (e.g. data on flows, depths, pH, temperature, etc.) interconnected with the physicochemical properties of the chemical compounds under various conditions with the final aim of predicting their fate in the environment. According to [10], this can be an inexpensive and suitable approach for setting the limits for discharges in the environment of certain chemical compounds, and since the initial parameter description has been set up and validated by in situ and laboratory data, it can be studied with a minimum set of analysis (e.g., only the quantification of chemical compound inputs to the ecosystem) [10].
