Interactions isoboles

For binary mixtures, a straight line (isobole) is produced joining Di and D2 and passing through di, d-2). The interaction index (Cl) is 1, <1, or >1 when the combinations show zero interaction, synergism, or antagonism using dose addition, respectively. 

One difficulty in using this approach is to determine when a specific Cl actually deviates from 1 (additivity), as the method of isoboles as developed does not include measures to decide whether deviations from the line of additivity are systematic or simply due to chance or experimental error (Cassee et al. 1998). One way of dealing with this problem is to calculate confidence intervals for the iso-effective doses of the single compounds and to add a confidence belt to the line of additivity (Kortenkamp and Altenburger 1998). This envelope of additivity is an area in which those combinations of two compounds are lying that has a specific effect and may reasonably be considered as showing no interaction (for details see Cassee et al. 1998). 

These interactive effects may be visualized graphically as isoboles (Fig. 2.3) or alternatively, there are simple formulae, which may be used for detecting them ... 

Siihnel J. 1992. Assessment of interaction of biologically active agents by means of the isobole approach fundamental assumptions and recent developments. ACES 4 35 14. 

More recently Brochot et al. [89] reported an extension of the isobolographic approach to interaction studies for convulsant interaction among pelloxacin, norfloxacin, and theophylline in rats. Their contribution is unique in that they started out by explaining pharmacodynamic interactions for two drugs, but then extended the approach to derive an isobol for three drug interaction. In addition they included Bayesian analysis and developed a population model with Markov chain Monte Carlo methods. 

Response Surface Model A dose-response surface is an extension of dose-response lines (isobols) to three dimensions. In this representation there can be a dose-response surface representing additivity and surfaces above and below suggesting deviation from additivity. Tam et al. [90] studied the combined pharmacodynamic interactions of two antimicrobial agents, meropenem and tobramycin. Total bacterial density data, expressed as CFU (colony forming units), were modeled using a three-dimensional surface. Effect summation was used as the definition of additivity (null interaction hypothesis) and the pharmacodynamic model was assumedi to take the functional form... 

In the absence of empirically intensive studies of cross adaptation (Kohbara and Ca-prio 1996) there currently are no models that accurately predict the nature of the interaction of mixtures, regardless of the sensory system studied or bioassay used. In the absence of any theoretical models that describe the interactions of agents, investigators have used descriptive models based on data. Isobole approaches use averaging models to define the null condition of no interaction, then go on to provide a descriptive index of enhancement or suppression using concentrations, responses, and empirical concentration-response relationships (Suhnel, 1993). This approach is useful because it can be applied to systems for which mechanistic information driving the concentration-response is not available (see methods). 

Averaging models typically end here, implying that an animal s response to a mixture can be estimated from its response to the single component concentration response curves. The isobole approach allows for the description of deviation from independence by defining an interaction index, 7, where at concentration, /, / is defined as... 

The ADM is valid for studying the interactions of herbicides with other herbicides or nonherbicides that exhibit similar action. Under the assumptions of the ADM, the growth responses of a test plant to the joint application of two components of a herbicide mixture are equated to the sum of the responses to each chemical tested separately.Thus, the predicted dose-response relationships for a herbicide mixture using the ADM are such that if one component of the mixture is replaced at a constant proportion by the other, the predicted response remains unchanged. Methods developed for the prediction of plant responses to herbicide mixtures using the ASM include the isobole method, the ANOVA method, and the two-parameter method. " ... 

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