Department of Physics and Nuclear Engineering, United States Military Academy, West Point, NY, 10996, USA.
Department of Mathematical Sciences, United States Military Academy, West Point, NY, US.
Int J Obes (Lond). 2022 Dec;46(12):2095-2101. doi: 10.1038/s41366-022-01205-0. Epub 2022 Aug 20.
When a lifestyle intervention combines caloric restriction and increased physical activity energy expenditure (PAEE), there are two components of energy balance, energy intake (EI) and physical activity energy expenditure (PAEE), that are routinely misreported and expensive to measure. Energy balance models have successfully predicted EI if PAEE is known. Estimating EI from an energy balance model when PAEE is not known remains an open question.
The objective was to evaluate the performance of an energy balance differential equation model to predict EI in an intervention that includes both calorie restriction and increases in PAEE.
The Antonetti energy balance model that predicts body weight trajectories during weight loss was solved and inverted to estimate EI during weight loss. Using data from a calorie restriction study that included interventions with and without prescribed PAEE, we tested the validity of the Antonetti weight predictions against measured weight and the Antonetti EI model against measured EI using the intake-balance method at 168 days. We then evaluated the predicted EI from the model against measured EI in a study that prescribed both calorie restriction and increased PAEE.
Compared with measured body weight at 168 days, the mean (±SD) model error was 1.30 ± 3.58 kg. Compared with measured EI at 168 days, the mean EI (±SD) model error in the intervention that prescribed calorie restriction and did not prescribe increased PAEE, was -84.9 ± 227.4 kcal/d. In the intervention that prescribed calorie restriction combined with increased PAEE, the mean (±SD) EI model error was -155.70 ± 205.70 kcal/d.
The validity of the newly developed EI model was supported by experimental observations and can be used to determine EI during weight loss.
当生活方式干预结合热量限制和增加体力活动能量消耗（PAEE）时，能量平衡有两个组成部分，即能量摄入（EI）和体力活动能量消耗（PAEE），这两个部分通常会被错误报告，且测量费用昂贵。如果已知 PAEE，则能量平衡模型可以成功预测 EI。当不知道 PAEE 时，从能量平衡模型中估计 EI 仍然是一个悬而未决的问题。
评估能量平衡微分方程模型在包括热量限制和增加 PAEE 的干预中预测 EI 的性能。
解决 Antonetti 能量平衡模型，该模型预测减肥期间的体重轨迹，并将其反转以估计减肥期间的 EI。使用包括有和没有规定 PAEE 的干预的热量限制研究的数据，我们使用摄入平衡法在 168 天内将 Antonetti 体重预测值与实测体重进行比较，将 Antonetti EI 模型与实测 EI 进行比较，然后在规定热量限制和增加 PAEE 的研究中评估模型预测的 EI 与实测 EI 的比较。
与 168 天的实测体重相比，模型误差的平均值（±SD）为 1.30±3.58kg。与 168 天的实测 EI 相比，在规定热量限制但不规定增加 PAEE 的干预中，EI 模型的平均（±SD）误差为-84.9±227.4kcal/d。在规定热量限制和增加 PAEE 的干预中，EI 模型的平均（±SD）误差为-155.70±205.70kcal/d。
新开发的 EI 模型的有效性得到了实验观察的支持，可以用于确定减肥期间的 EI。
