Effect of incretin concentration alone. Two tests of the hypothesis that an increase in incretin concentration alone can explain the fall in glucose level and homeostatic model assessment insulin resistance (HOMA-IR) immediately after surgery. The three lower curves show the scaled glucose concentration x
as a function of the factor r by which active incretins are increased. (Reported values of r range from 1 to more than 10, with most ≲ 2 or 3.) These curves correspond to three assumptions regarding the incretin contribution to insulin production: 50% for the top curve, 67% for the middle curve, and 100% for the bottom curve. Even in the most favorable scenarios, the decrease is insufficient to explain all the observations. The horizontal line at the top is the scaled product glucose × insulin, or x
, which is a measure of insulin resistance analogous to HOMA-IR. As found in Eq. (33), it is constant for all scenarios – i.e., for all values of r and all percentages for the incretin contribution. In other words, the incretin mechanism alone predicts no decrease whatsoever in this quantity. Many observations, on the other hand, show a very substantial drop in HOMA-IR immediately or very soon after surgery.