Christiansen Edmund, Swann Andrew, Sørensen Thorkild I A
Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark.
J Theor Biol. 2008 Oct 21;254(4):731-6. doi: 10.1016/j.jtbi.2008.07.004. Epub 2008 Jul 15.
Most people maintain almost constant body weight over long time with varying physical activity and food intake. This indicates the existence of a regulation that works well for most individuals. Yet some people develop obesity, indicating that this regulation sometimes fails. The difference between the two situations is typically an energy imbalance of about 1% over a long period of time.
Weight gain increases basal metabolic rate. Weight gain is often associated with a decrease in physical activity, although not to such an extent that it prevents an increase in total energy expenditure and energy intake. Dependent on the precise balance between these effects of weight gain, they may make the body weight unstable and tend to further promote weight gain. With the aim of identifying the thresholds beyond which such self-promoting weight gain may take place, we develop a simple mathematical model of the body as an energy-consuming machine in which the changes in physical activity and food intake are described as feedback effects in addition to the effect of the weight gain on basal metabolic rate. The feedback parameters of the model may differ between individuals and only in some cases do they take values that make weight gain self-promoting.
We determine the quantitative conditions under which body weight gain becomes self-promoting. We find that these conditions can easily be met, and that they are so small that they are not observable with currently available techniques. This phenomenon encourages emphasis on even minor changes in food intake and physical activity to abate or stop weight gain.
大多数人在长时间内尽管身体活动和食物摄入量有所变化,但体重几乎保持恒定。这表明存在一种对大多数人有效的调节机制。然而,有些人会患上肥胖症,这表明这种调节机制有时会失效。这两种情况之间的差异通常是长期存在约1%的能量失衡。
体重增加会提高基础代谢率。体重增加通常与身体活动减少有关,尽管减少的程度不至于阻止总能量消耗和能量摄入的增加。取决于体重增加的这些影响之间的精确平衡,它们可能会使体重不稳定,并倾向于进一步促进体重增加。为了确定可能发生这种自我促进体重增加的阈值,我们构建了一个简单的人体数学模型,将人体视为一台耗能机器,其中除了体重增加对基础代谢率的影响外,身体活动和食物摄入的变化被描述为反馈效应。该模型的反馈参数可能因人而异,只有在某些情况下,它们才会取使体重增加具有自我促进作用的值。
我们确定了体重增加变得具有自我促进作用的定量条件。我们发现这些条件很容易满足,而且非常微小,以至于用目前可用的技术无法观察到。这种现象促使人们强调即使是食物摄入量和身体活动的微小变化,以减轻或阻止体重增加。