In quantitative situations, the Y-axis often is designated by percentages, which refer to the percentage of exposed individuals registering a standard response (which may be death, as in ). Such a curve is referred to as a quantal dose–response curve, distinguishing it from a graded dose–response curve, where response is continuous (either measured, or by judgment). The Hill equation can be used to describe dose–response relationships, for example ion channel-open-probability vs. ligand concentration. Dose is usually in milligrams, micrograms, or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures. Other dose units include moles per body-weight, moles per animal, and for dermal exposure, moles per square centimeter. Limitations The concept of linear dose–response relationship, thresholds, and all-or-nothing responses may not apply to non-linear situations. A threshold model or linear no-threshold model may be more appropriate, depending on the circumstances. A recent critique of these models as they apply to endocrine disruptors argues for a substantial revision of testing and toxicological models at low doses because of observed non-monotonicity, i.e. U-shaped dose/response curves. Dose–response relationships generally depend on the exposure time and exposure route (e.g., inhalation, dietary intake); quantifying the response after a different exposure time or for a different route leads to a different relationship and possibly different conclusions on the effects of the stressor under consideration. This limitation is caused by the complexity of biological systems and the often unknown biological processes operating between the external exposure and the adverse cellular or tissue response. Schild analysis Schild analysis may also provide insights into the effect of drugs. See also Arndt–Schulz rule Ceiling effect (pharmacology) Certain safety factor Hormesis Pharmacodynamics Spatial epidemiology Weber–Fechner law Dose fractionation References External links Online Tool for ELISA Analysis Online IC50 Calculator Ecotoxmodels A website on mathematical models in ecotoxicology, with emphasis on toxicokinetic-toxicodynamic models CDD Vault, Example of Dose-Response Curve fitting software Pharmacodynamics Toxicology