System Identification Approaches For Energy Intake Estimation: Enhancing Interventions For Managing Gestational Weight Gain

Abstract

Excessive maternal weight gain during pregnancy represents a major public health concern that calls for novel and effective gestational weight management interventions. In Healthy Mom Zone (HMZ), an on-going intervention study, energy intake underreporting has been found to be an important consideration that interferes with accurate weight control assessment, and the effective use of energy balance models in an intervention setting. In this paper, a series of estimation approaches that address measurement noise and measurement losses are developed to better understand the extent of energy intake underreporting. These include back-calculating energy intake from an energy balance model developed for gestational weight gain prediction, a Kalman filtering-based approach to recursively estimate energy intake from intermittent measurements in real-time, and an approach based on semi-physical identification principles which features the capability of adjusting future self-reported energy intake by parameterizing the extent of underreporting. The three approaches are illustrated by evaluating with participant data obtained through the HMZ intervention study, with the results demonstrating the potential of these methods to promote the success of weight control. The pros and cons of the presented approaches are discussed to generate insights for users in future applications.

Keywords: Kalman filter; State estimation; intermittent measurements; obesity; semi-physical identification; system identification; underreporting; weight interventions.

Figures

Fig. 1:

Weight predictions from the energy balance model according to (1) using data from two representative participants in the Healthy Mom Zone intervention study. These show evidence of significant underreporting of energy intake. Participant A is an OW woman from the intervention group and Participant B (OW) from the control group. The self-reported EI are obtained from a smartphone app (MyFitnessPal) and PA is objectively monitored with a wrist-worn accelerometer (Jawbone). Additional information on data collection is described in Section II.B.

Fig. 2:

Block diagram depicting a closed-loop intervention for gestational weight gain, and how estimation approaches to energy intake as developed in this paper (indicated in the blue box) can be incorporated within the system. Energy intake estimates as well as the filtered weight measurements resulting from these estimators can be used by a hybrid model predictive control (HMPC) algorithm to determine optimized intervention dosages of intervention components (such as healthy eating active learning, physical activity active learning, goal setting), as described in [23], [24].

Fig. 3:

EI back-calculation results for the two representative participants from the HMZ intervention study. Comparing the measured W (circles) with the simulated W (dashed) using back-calculated EI, it provides support for the validity of the EI estimates. BMI: body mass index; GA: gestational age.

Fig. 4:

Results of estimating the EI using Kalman filtering for two HMZ participants. The results indicate that underreporting of EI can be identified for most of the time; however, estimation accuracy is compromised when the weight measurement is missing for multiple consecutive days. The prediction bias is indicated with root mean square error (RMSE). Vertical black lines in the GWG plot indicate the days of missing GWG measurements.

Fig. 5:

Kalman filtering performance for Participant B for two-state estimation. In this case, the estimation of the EI is implemented simultaneously with noise filtering for the PA measurements. Vertical black lines in the GWG plot indicate the days of missing GWG measurements. RMSE stands for root mean square error.

Fig. 6:

Block diagram of the regression model used for the development of the semi-physical identification approach. nW, nEIrept and nEIest indicate the noise in the measured W, self-reported EI, and estimated EI, respectively.

Fig. 7:

Results of semi-physical identification of EI for two HMZ participants. (a) Estimation results based on Model C for an intervention Participant A on validation data set only. (b) Results for a control Participant B based on Model C (residual demonstrating non-stationarity). (c) Results based on Model F for the control Participant B (non-stationary trend in the residuals removed).