Functional regression for data fusion and indirect measurements of physiological variables collected by wearable sensor systems and indirect calorimetry Andrei Gribok, William Rumpler Food Components and Health Laboratory, Beltsville Human Nutrition Research Center, Agricultural Research Service, United States Department of Agriculture, Beltsville, MD, 20705 USA. Reed Hoyt, Mark Buller Biophysics and Biomedical Modeling Division, US Army Research Institute of Environmental Medicine, Natick, MA, 01760 USA Abstract— The paper describes application of different types of functional regression for analysis and modeling of the data collected by wearable sensor systems. The data have been recorded from human subjects while they were staying in whole room calorimeter chamber for 48 hours. This allowed very accurate measurements of their oxygen consumption, energy expenditure and substrate oxidation. These physiological parameters are notorious for their inaccuracy when measured in field conditions. The subjects wore two types of body sensors: the Hidalgo Equivital™ (Cambridge, UK) physiological monitors with a telemetry thermometer pill and iPro Professional Continuous Glucose Monitoring System (CGMS) (Medtronic MiniMed, Inc, Northridge, CA). The data collected by these two systems and by the calorimeter chamber were subsequently analyzed off-line using the functional regression techniques. The energy expenditure, substrate oxidation, and body core temperature were used as response variables, while heart rate, respiratory rate, subcutaneous glucose concentration, and skin temperature were used as predictors. The results show that the 24-hours and instantaneous energy expenditure values can be inferred from instantaneous measurements of heart rate, respiratory rate and glucose concentrations. Also, the body core temperature can be inferred from heart rate, respiratory rate, glucose concentration, and skin temperature. The substrate oxidation was the most difficult parameter to infer and it can only be accomplished during the exercise activity. Keywords—functional regression; inference; smoothing; wearable sensors I. INTRODUCTION Recent advances in the ability to monitor physiology variables have resulted from the development of new biosensors and information-processing capabilities. These capabilities have a direct impact on how closely a person’s state can be monitored during civilian activities or military operations, including the possibility of predicting changes in many vital physiological variables, such as body core temperature, heart and respiratory rates, and even such subtleties as level of alertness and performance. The technological breakthroughs in the development of hardware and ｿrmware were also accompanied by an equally profound and signiｿcant progress in such ｿelds as data mining, machine learning, and signal processing. New technologies to collect and store relatively large amounts of physiological data in the ｿeld allow researchers to explore new opportunities in data- driven methods to forecast physiological variables and status. Many data sets collected by wearable body sensor networks represent variation of one variable as a function of another variable, usually time. For example, subcutaneous glucose concentration recorded as a function of time, heart and respiratory rates as function of activity, core body temperature as function of heart rate. While being very different physiological measurands they have one thing in common: they represent smooth variations of physiological variables as functions of some parameters. The functional data analysis (FDA) makes use of such “functionality” to reveal the sources of variations and cause-effect relationships in the data. The wearable body sensors offer a unique opportunity in applying FDA since they allow collecting many sensor modalities concurrently and exploiting correlation in the data for model building and verification. II. DATA COLLECTION A. Test Subjects We enrolled nine young, generally lean, healthy, non- smoking male volunteers who reported no regular physical activity or exercise training within the previous six months (23 ± 1.2 years, 176.8 ± 3.7 cm, 76.2 ± 3.6 kg, 17.2 ± 2.3 percent body fat and BMI of 24 ± 1.1). Each subject completed two 48-h metabolic chamber measurements, for each the first day serving as a control day and the exercise experiment taking place on the second day. This gave us total 17 calorimeter sessions, since one subject quit after the first session. Throughout the 48-h protocol, we obtained continuous measurements of indirect calorimetry, core body temperature (BT), heart rate (HR), respiratory rate (RR), skin temperature (ST), and subcutaneous glucose concentration. We utilized 40 min high-intensity resistance exercise to generate a stimulus that has qualities of both aerobic and resistance exercise. Informed consent was signed by all participants. This study protocol was approved by the internal review board of the George Washington University Medical Center. U.S. Government work not protected by U.S. copyright