The differential aspects of the linear isobole in the study of combined action of agents

Although the isobologram is presently the most widely used method of analysis for combined effects of agents, there are several different interpretations of the linear isobole in regard to its use as a criterion of interaction. An investigation of the differential aspects of the linear isobole relation may cast some light in this regard. By conceptual extension of the present single effect level (i.e. effect-point) relation of the linear isobole to an effect-neighbourhood relation in which the linear isobole holds over a small continuous range of effect levels, the mathematical differential of the linear isobole can be developed and investigated. This differential aspect provides some useful insights into the implication and interpretation of the linear isobole relation when used as a general criterion in agent interaction studies. It can also serve as the mathematical basis for the formulation of analytic schemes in which the linear isobole relation is applicable over a continuous range of effect levels.