Vol. 289, Issue 1, 8-13, April 1999

Response Surface Analysis of Synergism Between Morphine and Clonidine¹

Ronald J. Tallarida, Dennis J. Stone, Jr., Jeffrey D. McCary and Robert B. Raffa

Temple University School of Medicine (R.J.T., J.D.M.) and School of Pharmacy (D.J.S., R.B.R.), Philadelphia, Pennsylvania

Graded doses of morphine sulfate and clonidine hydrochloride were administered intrathecally to mice that were then tested for antinociception in the 55°C tail immersion test. The dose-effect relations of each compound were used in calculations that permitted the construction of a three-dimensional plot of the expected additive effect (vertical scale) against the planar domain of dose pairs representing combinations administered simultaneously. This additive response surface became the reference surface for viewing the actual effects produced by three different fixed-ratio combinations of the drugs that were used in our tests. Each combination produced effects significantly greater than indicated by the additive surface, thereby illustrating marked synergism and a method for quantifying the synergism. This quantification, measured by the value of the interaction index (), was found to be dependent on the fixed-ratio combination; accordingly, the actual response surface could not be described by a single value of the index . Furthermore, we found that application of the common method of isoboles gave estimates of the index that agreed well with those obtained from the more extensive surface analysis. These results confirm earlier studies, which found synergism for these drugs while also providing surface views of additivity and synergism that form the basis of isobolographic analysis.