Mathematical modeling predicting toxicity

Many wastewater flows in industry can not be treated by standard aerobic or anaerobic treatment methods due to the presence of relatively low concentration of toxic pollutants. Ozone can be used as a pretreatment step for the selective oxidation of these toxic pollutants. Due to the high costs of ozone it is important to minimise the loss of ozone due to reaction of ozone with non-toxic easily biodegradable compounds, ozone decay and discharge of ozone with the effluent from the ozone reactor. By means of a mathematical model, set up for a plug flow reactor and a continuos flow stirred tank reactor, it is possible to calculate more quantitatively the efficiency of the ozone use, independent of reaction kinetics, mass transfer rates of ozone and reactor type. The model predicts that the oxidation process is most efficiently realised by application of a plug flow reactor instead of a continuous flow stirred tank reactor. 

This chapter first reviews and discusses selected research on local dose aspects of ozone toxicity, the morphology of the respiratoty tract and mucus layer, air and mucus flow, and the gas, liquid, and tissue components of mathematical models. Next, it discusses the approaches and results of the few models that exist. A similar review was recently done to defme an analytic framework for collating experiments on the effects of sulfur oxides on the lung. Pollutant gas concentrations are generally stated in parts per million in this chapter, because experimental uptake studies are generally quoted only to illustrate behavior predicted by theoretical models. Chapter 5 contains a detailed discussion of the conversion from one set of units to another. 

It is interesting to note that a number of researchers have attempted, more or less successfully, to construct reliable mathematical models which combine structural elements and experimental data to predict the toxicities of new substances not yet experimentally tested for humans and other species.110152 Furthermore pharmacology, toxicity, metabolism and enzyme-inhibiting effects of fluorine-containing aromatic systems (e.g., anilines, ben-zothiadiazines, butyrophenones, corticoids, phenothiazines, steroids, uracils) have been discussed in depth in the literature.153-156... 

There are various mathematical models that can be used to describe and analyze experimental data (Scholze et al. 2001). In addition to these curve-fitting approaches, response surface models are also available (e.g., Greco et al. 1995), but these are suitable primarily for the analyses of experimental data, rather than for predictive purposes. As an example, Altenburger et al. (2004) applied both concentration addition and response addition and observed that the combined effect of a 3-compound mixture out of 10 identified sediment toxicants was sufficient to explain the observed combined effect of the more complex mixture. For identifying remediation priorities in site-specific assessment of complex contamination, this approach has great potential. 

In addition to using PMs, predictions of toxic hazard can also be made by using structure-activity relationships (SARs). A quantitative structure-activity relationship (QSAR) can be defined as any mathematical model for predicting biological activity from the structure or physicochemical properties of a chemical. In this chapter, the premodifer quantitative is used in accordance with the recommendation of Livingstone (1995) to indicate that a quantitative measure of chemical structure is used. In contrast, a SAR is simply a (qualitative) association between a specific molecular (sub)structure and biological activity. 

Abuzaid, N. S. and G. Nakhla (1997). Predictability of the homogeneous surface diffusion model for activated carbon adsorption kinetics formulation of a new mathematical model, J. Environment. Science Health, Part A Environment. Eng. Toxic Hazardous Substance Control. 32, 7, 1945-1961. 

In the 1980s, investigators at NIST began examining the possibility of combining the analytical chemical method with the animal exposure approach to develop empirical mathematical models to predict the toxicity. These predictions were based... 

To develop a bioanalytical screening test and a mathematical model which would predict whether a material would produce extremely toxic or unusually toxic combustion products. 

Computational modeling is a powerful tool to predict toxicity of drugs and environmental toxins. However, all the in silico models, from the chemical structure-related QSAR method to the systemic PBPK models, would beneht from a second system to improve and validate their predictions. The accuracy of PBPK modeling, for example, depends on precise description of physiological mechanisms and kinetic parameters applied to the model. The PBPK method has primary limitations that it can only predict responses based on assumed mechanisms, without considerations on secondary and unexpected effects. Incomplete understanding of the biological mechanism and inappropriate simplification of the model can easily introduce errors into the PBPK predictions. In addition values of parameters required for the model are often unavailable, especially those for new drugs and environmental toxins. Thus a second validation system is critical to complement computational simulations and to provide a rational basis to improve mathematical models. 

We expect that these novel cell culture systems, coupled with predictions from in silico and mathematical modeling, will provide new insights into the toxicity of environmental and pharmaceutical chemicals, expand our understanding of toxicological mechanisms, and improve prediction of human clinical responses. 

Kinetics Considerations. Kinetics concepts and data concerning halocarbon sources and sinks can be used for a variety of purposes. For example, such information is required in mathematical models to evaluate the fate and exposure concentrations of low-volatility toxic organohalogens in water (18, 19). Moreover, kinetics relationships and data concerning physical, chemical, and biological processes are needed to predictively model aquatic sinks of volatile halocarbons (11). 

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