Egan Aoife M, Rayman John F, Collins Adam L
Faculty of Health & Medical Sciences, University of Surrey, Guildford, United Kingdom of Great Britain and Northern Ireland.
Department of Mathematics, University of Surrey, Guildford, United Kingdom of Great Britain and Northern Ireland.
J Nutr Sci. 2024 Dec 12;13:e92. doi: 10.1017/jns.2024.85. eCollection 2024.
Weight loss results in obligatory reductions in energy expenditure (EE) due to loss of metabolically active fat-free mass (FFM). This is accompanied by adaptive reductions (i.e. adaptive thermogenesis) designed to restore energy balance while in an energy crisis. While the '3500-kcal rule' is used to advise weight loss in clinical practice, the assumption that EE remains constant during energy restriction results in a large overestimation of weight loss. Thus, this work proposes a novel method of weight-loss prediction to more accurately account for the dynamic trajectory of EE. A mathematical model of weight loss was developed using ordinary differential equations relying on simple self-reported inputs of weight and energy intake to predict weight loss over a specified time. The model subdivides total daily EE into resting EE, physical activity EE, and diet-induced thermogenesis, modelling obligatory and adaptive changes in each compartment independently. The proposed model was tested and refined using commercial weight-loss data from participants enrolled on a very low-energy total-diet replacement programme (LighterLife UK, Essex). Mathematical modelling predicted post-intervention weight loss within 0.75% (1.07 kg) of that observed in females with overweight or obesity. Short-term weight loss was consistently underestimated, likely due to considerable FFM reductions reported on the onset of weight loss. The best model agreement was observed from 6 to 9 weeks where the predicted end-weight was within 0.35 kg of that observed. The proposed mathematical model simulated rapid weight loss with reasonable accuracy. Incorporated terms for energy partitioning and adaptive thermogenesis allow us to easily account for dynamic changes in EE, supporting the potential use of such a model in clinical practice.
由于代谢活跃的去脂体重（FFM）减少，体重减轻会导致能量消耗（EE）必然减少。这伴随着适应性降低（即适应性产热），旨在在能量危机期间恢复能量平衡。虽然“3500千卡规则”在临床实践中用于指导减肥，但能量限制期间EE保持不变的假设导致对体重减轻的大幅高估。因此，这项工作提出了一种新的减肥预测方法，以更准确地考虑EE的动态变化轨迹。利用常微分方程建立了一个减肥数学模型，该模型依赖于简单的自我报告的体重和能量摄入输入来预测特定时间内的体重减轻。该模型将每日总EE细分为静息EE、身体活动EE和饮食诱导产热，分别对每个部分的必然变化和适应性变化进行建模。使用来自参加极低能量全膳食替代计划（英国埃塞克斯郡的LighterLife）的参与者的商业减肥数据对所提出的模型进行了测试和完善。数学建模预测的干预后体重减轻与超重或肥胖女性观察到的体重减轻相差在0.75%（1.07千克）以内。短期体重减轻一直被低估，可能是由于减肥开始时报告的FFM显著减少。在6至9周时观察到最佳的模型一致性，预测的最终体重与观察到的体重相差在0.35千克以内。所提出的数学模型以合理的准确性模拟了快速减肥。纳入能量分配和适应性产热的术语使我们能够轻松考虑EE的动态变化，支持这种模型在临床实践中的潜在应用。
