A mathematical model of weight change with adaptation

Diana M. Thomas; Ashley Ciesla; James A. Levine; John G. Stevens; Corby K. Martin; Diana M. Thomas; Ashley Ciesla; James A. Levine; John G. Stevens; Corby K. Martin

doi:10.3934/mbe.2009.6.873

Mathematical Biosciences and Engineering

2009, Volume 6, Issue 4: 873-887. doi: 10.3934/mbe.2009.6.873

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A mathematical model of weight change with adaptation

1.
Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043
2.
Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043
3.
Department of Medicine, Endocrine Research Unit, Mayo Clinic and Mayo Foundation, Rochester, MN 55905
4.
Pennington Biomedical Research Center, Ingestive Behavior Laboratory, Baton Rouge, LA 70808

Received: 01 November 2008 Accepted: 29 June 2018 Published: 01 September 2009
MSC : Primary: 58F15, 58F17; Secondary: 53C35.

As obesity and its related health problems grow around the world, efforts to control and manage weight is increasing in importance. It is well known that altering and maintaining weight is problematic and this has led to specific studies trying to determine the cause of the difficulty. Recent research has identified that the body reacts to forced weight change by adapting individual total energy expenditure. Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. Forward time simulations of the model compare well with mean data in both overfeeding and calorie restriction studies.

Keywords:

Citation: Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin. A mathematical model of weight change with adaptation[J]. Mathematical Biosciences and Engineering, 2009, 6(4): 873-887. doi: 10.3934/mbe.2009.6.873

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Abstract

As obesity and its related health problems grow around the world, efforts to control and manage weight is increasing in importance. It is well known that altering and maintaining weight is problematic and this has led to specific studies trying to determine the cause of the difficulty. Recent research has identified that the body reacts to forced weight change by adapting individual total energy expenditure. Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. Forward time simulations of the model compare well with mean data in both overfeeding and calorie restriction studies.

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