Abstract
Introduction: Weight-loss results in obligatory reductions in energy expenditure (EE) due to
loss of metabolically active fat-free mass (FFM). This is often accompanied by adaptive
reductions designed to restore energy balance whilst in energy crisis. Such declines are
suggested to be amplified during rapid weight-loss. 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. Subsequently, obligatory and adaptive REE reductions will be quantified during a
total-diet replacement programme (TDR; 600–810 kcal/day).
Methods: A mathematical model of weight-loss was developed using ordinary differential
equations relying on simple inputs of weight and energy intake to predict weight-loss over a
specified time. The proposed model was tested and refined using: (i) retrospective data from
a commercial weight management company (ii) secondary data from a randomised controlled
trial and (iii) prospective data from a nutrition intervention trial.
Results: Mathematical modelling predicted post-intervention weight-loss within 0.80% of
that observed in overweight and obese females. Short-term weight-loss was consistently
underestimated, due to considerable FFM reductions (60% of total weight-loss), largely
explained by fluid losses. The proportion of weight lost as FFM declined thereafter. Of the
associated REE reductions, half was explained by metabolic adaptation detected within 2
weeks of TDR treatment. The best model agreement was observed in 6–9-week interventions,
where predicted end-weight was within 0.6 kg of that observed.
Conclusion: These results highlight the metabolic processes determining short-term
weight-loss and provide evidence for an immediate adaptive response to energy deficit. The
proposed mathematical model simulates weight-loss during a TDR intervention with reasonable
accuracy supporting the potential application in clinical weight management.