In collaboration with Kevin Hall, I have been interested in modeling how the body partitions the macronutrients of the diet into lean and fat body tissue. Using empirical cross-sectional data of the relationship between fat and lean mass, we have developed an expression for how substrate utilization adapts to changes of diet, energy expenditure, and body fat so that energy imbalances produce the observed changes of body composition. The theoretical prediction matches experimental data without the use of free parameters. We used the model to compare the total US food supply with the estimated energy expended by the population and showed that the food supply is exceeding the demand. The results predict that the US obesity epidemic is due to a push effect of an excess supply on food leading to a progressive increase in food waste. Recently, we have analyzed global data and found evidence for a push effect in other countries and in particular developed countries. Hall and I have also shown how measurements of body mass can be used to infer food intake. The model also shows that the time scale to approach steady state when diet is changed is very long, on the order of years. This slow response may partially explain why it is so hard to maintain weight loss. People do not receive timely feedback on their diet performance. We have also resolved the long standing paradox of why body weight is maintained precisely even when food intake wildly fluctuates. We showed that the long time constant smooths the intake fluctuations and used stochastic calculus to calculate a formula. In collaboration with Boyd Swinburn and Nancy Butte, we have generalized the model to apply to growing children over the age of 5. We have used the growth model to predict food intake for children consuming sugar sweetened beverages and those with a noncaloric substitute. We found that children with higher BMI were less likely to compensate for the reduction in calories. This may indicate that the caloric sensing mechanism in overweight children may not be functioning optimally. We have recently extended the model to apply from birth. In collaboration with Anne Sumner and Vipul Periwal, we developed a time dependent mathematical model of the suppression of lipolysis by insulin. The model can be used to develop a quantitative measure for insulin's effect on serum free fatty acids akin to insulin sensitivity for glucose. We have also used the model to compare differences in free fatty acid dynamics between white and black women. In collaboration with Vipul Periwal, we have developed a new Bayesian scheme to estimate insulin secretion. We have also applied the model to adolescents. We have recently augmented the model to account for ingested meals. We are currently using the model to estimate insulin secretion rates in collaboration with Stephanie Chung.
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