An analysis of dietary restraint and obesity using a dynamic model of cumulative food intake curves

Abstract

BackgroundIn 1980, Kissileff et al. developed the universal eating monitor permitting investigators to calculate cumulative food intake curves. In this landmark study, cumulative food intake curves were fit using linear and quadratic functions. Yet, these models are artificial since cumulative food intake will never decrease, but rather saturate toward a carrying capacity.Methods: We used the Verhulst differential equation model that describes rapid growth followed by saturation to a carrying capacity and estimated model parameters for different food intake curves. The Verhulst model consists of two parameters, r (exponential growth rate) and the carrying capacity (K). Model parameters were calculated for unrestrained and restrained eaters who were guided to eat 1) as much as they feel comfortable with and 2) and as much as you can.Results: Model parameters were r=0.04, K=1500 g for the unrestrained eat as much as you can condition, and r=0.14, K=450 g for the unrestrained eat as much as you feel comfortable with condition. For restrained eaters, the eat as much as you can condition yielded r=0.05, K=1100 g while the eat as much as you feel comfortable with condition generated the parameters r=0.06, K=800 g.ConclusionNormalizing all cumulative food intake curves differentiated unrestrained eaters who were directed to eat as much as they could from all other scenarios. Mechanistically, the exponential growth rate parameter, r, associated with early increases in the rate of food intake was nearly three times larger than growth rates in all other cases. Identifying and classifying individuals who exhibit a high value of r can be useful for detecting and potentially changing eating rates to decrease energy intake.