# Real-Time Model Predictive Control of Human Bodyweight Based on Energy Intake
## 3 Results and Discussion
### Time-Variant Parameters Models
Biologically, it is expected that the energy efficiency will vary with time and the current efficiency should be more relevant than the efficiency in past instances. Thus, it seems that the DLR model is not capturing fully the expected biological behavior of the process. In contrast, the DARX model shows that increasing the window size improves the forecasting performance, but only until a certain range. Once this range is exceeded, the forecasting properties worsen again. This is expected, as the sliding time window with a fixed size should help in removing the impact of obsolete data in the model [47]. Thus, this is more in line with what it is expected in terms of the biological process under study. Furthermore, it can be seen that the optimal time window size changes according to the prediction horizon size. For instance, if the prediction horizon is raised to 4-5 weeks, thus over a month time, the MRPE error ranges between 2.5-3% and the optimal time window size range increases to 10-14 weeks. The prediction of bodyweight using a recursive linear regression approach based on time-variant parameters has been already tested on broiler chickens [47]. In that study, the lowest _MRPE_ reaches a value of 1.4% for a prediction horizon of 1 day and the highest _MRPE_ is 4.1% for a prediction horizon of 7 days, when broiler chickens are fed ad libitum [47]. These results illustrate that using time-variant parameters models to predict human bodyweight is highly accurate, improving the previous results. Lastly, it is important to mention that because little information on energy expenditure is known, the bodyweight predictions are based solely on energy intake. The data from the Minnesota starvation experiment include merely estimations of the resting energy expenditure on the week prior to the starvation phase and at the end of the starvation phase. Thus, calculating the weekly energy balance is not possible. There are several models in literature that attempt to address this characteristic during a weight program intervention by using complex mechanistic models based on systems of one dimensional differential equations [28; 29; 31; 32]. Although these theoretical models resemble accurately the dynamic process of bodyweight change, the large amount of model parameters are estimated based on averages from population studies [32] and do not take into account the changes in the values of the model parameters throughout the experimental period [11]. In the modelling framework proposed in this study, not only the dynamic evolution through time, but also the dynamics induced by the impact of internal and external factors in the model parameters are taken into account implicitly by the model. This allows designing more compact models, reducing greatly their complexity while capturing the most relevant dynamics of the process. In future, if both energy intake and expenditure would be available, a time-variant model in which both are used as inputs could be developed. Moreover, gathering regular information about the time course of fat body mass and lean body mass would allow developing a time-variant model, whose model parameters could be related to existing mechanistic equations describing bodyweight component changes in response to changes in energy intake and energy expenditure. On one hand, this would help dietitians to develop further the current mechanistic expressions to describe more accurately the bodyweight change process. On the other hand, it would enable them to evaluate and adapt in real-time the impact of the suggested dietary energy intake to achieve a desire bodyweight change at individualized patient level. In summary, these results show that a time-variant parameters model allows characterizing accurately the dynamics of a body weight change induced by a change in dietary energy intake. Using a window size of seven weeks of dietary energy intake allows forecasting bodyweight one-week ahead with a MRPE of 1.04% and four-weeks ahead with a MRPE of 2.53%.