Derivation of equations for the plateau principle and their application to changes in body mass index and insulin sensitivity after bariatric surgery

Abstract

We derive equations for a model called the plateau principle that describes an exponential approach to steady state. We test whether the general solution fits data for longitudinal changes in body mass index (BMI) and insulin sensitivity (HOMA) during 3 years after laparoscopic mini‐gastric bypass surgery (LMGB). In the general solution, k is a unique, first order rate parameter, t is time, and M0, Mt and Mss, respectively, are BMI or HOMA at baseline, at time t, and at steady state: urn:x-wiley:08926638:fsb2fasebj251supplement9871:equation:fsb2fasebj251supplement9871-math-0001 We show how to automate Microsoft Excel's Solver feature to fit the model to a large data set (n = 1069) obtained after LMGB. Three year follow‐up data for 97 patients with complete records show an exponential pattern for change in BMI for most individuals and for group averages. The model shows that the rate of change for HOMA is much greater than the rate of change in BMI (mean k ≅ 1.26 mo−1 vs. 0.25 mo−1) BMI stabilizes for most patients between 9–18 mo, whereas HOMA stabilizes in less than 6 mo. There is little or no difference in rates of change among most anthropometric measures, or in rates of change between female and male subjects. We conclude that the plateau model of Equation 1 can be applied to changes in BMI and some other anthropometric and functional measures after bariatric surgery. When model assumptions are valid, the model may also apply to changes in weight or functional capacity during weight loss caused by dieting, aerobic training, or by drug treatment. (Supported by Hatch project GEO00602 from the GA Agricultural Experiment Station).