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. 2018 Jun 1;124(6):1387-1402.
doi: 10.1152/japplphysiol.00837.2017. Epub 2018 Feb 8.

Individualized Estimation of Human Core Body Temperature Using Noninvasive Measurements

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Individualized Estimation of Human Core Body Temperature Using Noninvasive Measurements

Srinivas Laxminarayan et al. J Appl Physiol (1985). .
Free PMC article

Abstract

A rising core body temperature (Tc) during strenuous physical activity is a leading indicator of heat-injury risk. Hence, a system that can estimate Tc in real time and provide early warning of an impending temperature rise may enable proactive interventions to reduce the risk of heat injuries. However, real-time field assessment of Tc requires impractical invasive technologies. To address this problem, we developed a mathematical model that describes the relationships between Tc and noninvasive measurements of an individual's physical activity, heart rate, and skin temperature, and two environmental variables (ambient temperature and relative humidity). A Kalman filter adapts the model parameters to each individual and provides real-time personalized Tc estimates. Using data from three distinct studies, comprising 166 subjects who performed treadmill and cycle ergometer tasks under different experimental conditions, we assessed model performance via the root mean squared error (RMSE). The individualized model yielded an overall average RMSE of 0.33 (SD = 0.18)°C, allowing us to reach the same conclusions in each study as those obtained using the Tc measurements. Furthermore, for 22 unique subjects whose Tc exceeded 38.5°C, a potential lower Tc limit of clinical relevance, the average RMSE decreased to 0.25 (SD = 0.20)°C. Importantly, these results remained robust in the presence of simulated real-world operational conditions, yielding no more than 16% worse RMSEs when measurements were missing (40%) or laden with added noise. Hence, the individualized model provides a practical means to develop an early warning system for reducing heat-injury risk. NEW & NOTEWORTHY A model that uses an individual's noninvasive measurements and environmental variables can continually "learn" the individual's heat-stress response by automatically adapting the model parameters on the fly to provide real-time individualized core body temperature estimates. This individualized model can replace impractical invasive sensors, serving as a practical and effective surrogate for core temperature monitoring.

Keywords: Kalman filter; core body temperature; heat injury; individualized mathematical model; noninvasive measurements.

Figures

Fig. 1.
Fig. 1.
The proposed model for individualized core body temperature (Tc) estimation. The inputs to the model are the measured heart rate (HR), skin temperature (Ts), and physical activity (Ac) profiles from an individual and two environmental variables [ambient temperature (Ta) and relative humidity (RH)]. Step 1 (dark gray), the mathematical model uses the activity profile and environmental variables to estimate the HR and Ts. Step 2 (medium gray), the system computes the errors between the model-estimated HR and Ts and the corresponding measurements. Step 3 (light gray), the Kalman filter uses the errors to update six model parameters (α1, β, γ1, γ2, α3, and α4) and provide individualized real-time core temperature estimates. We fixed α2, the thermoregulatory rate constant of Tc, to a constant value. Parameter definitions: α1, the rate constant of HR; β, the gain in HR in response to Ac; γ1, the heat gain resulting from metabolic activity; γ2, the rate of heat transfer from the core to the skin compartment; α3, the rate of heat transfer from the skin to the environment via convection; and α4, the rate of heat transfer resulting from sweat evaporation.
Fig. 2.
Fig. 2.
Performance of the individualized model in predicting the Tc of one subject from study 1. A: activity profiles of the subject during heat tolerance tests at two Ta levels at a RH of 40%. BD: measured and estimated values of HR, Ts, and Tc, respectively, including the root mean squared error (RMSE) for the Tc estimates. Gaps in Ts and Tc data (C and D, respectively) are because of missing measurements.
Fig. 3.
Fig. 3.
Performance of the individualized model in predicting the Tc of one subject from study 2. A: activity profile during a heat tolerance test at an Ta of 40°C and a RH of 40%. BD: measured and estimated values of HR, Ts, and Tc, respectively, including the RMSE for the Tc estimates.
Fig. 4.
Fig. 4.
Performance of the individualized model in predicting the Tc of one subject from study 3. A: activity profiles of the subject while performing the cycle task under four experimental conditions at an Ta of 30°C and a RH of 50%. BD: measured and estimated values of HR, Ts, and Tc, respectively, including the RMSE for the Tc estimates.
Fig. 5.
Fig. 5.
Time profiles of the six adjustable model parameters (α1, β, γ1, γ2, α3, and α4) in the individualized model for the same subject from study 1 shown in Fig. 2. A: activity profiles of the subject during heat tolerance tests at two Ta levels at a RH of 40%. BG: time profiles of the six parameters.
Fig. 6.
Fig. 6.
Effect of missing HR data on model performance. Using data from the 22 unique subjects (34 profiles from the 3 studies) whose Tc exceeded 38.5°C, we generated 100 random realizations of missing HR data for each fraction (from 10 to 50%) of the total number of HR samples for each of the 34 profiles. We computed the RMSE between the measured and estimated Tc values for each random realization and missing HR fraction in each of the 34 profiles. We then computed and plotted the percentage increase in the RMSE as a function of the fraction of missing HR data for each of the 34 profiles. Values are medians and interquartile ranges.
Fig. A1.
Fig. A1.
Flowchart showing the initialization and subsequent steps of the Kalman filter algorithm for real-time Tc estimation (see text for symbol definitions). We initialized the algorithm with θ, σθ2, the HR and Ts measurement noise variances (matrix R), and the process noise variance σ2 estimated from the first 10 min of data for each subject. After initialization, the algorithm proceeded by using uk+1 to drive the mathematical model to estimate HR and Ts (estimation step). Next, by scaling the error ek+1 between the filtered measurements and the model-estimated HR and Ts by the Kalman gain Kk+1, the algorithm updated the model parameters and the Tc estimates at each time index (update step) until the end of the measured time series data.
Fig. D1.
Fig. D1.
HR error characteristics of the Samsung Gear S3 smartwatch. We compared the Gear S3 HR data obtained from 83 h of exercise recordings against the gold-standard polar chest-strap data (sampled at 15-s intervals). Top, medians and interquartile ranges of the errors plotted for each of the 10 beats/min bins. Bottom, no. of HR samples in each bin.
Fig. E1.
Fig. E1.
Time profiles of the six adjustable model parameters (α1, β, γ1, γ2, α3, and α4) in the individualized model for the same subject from study 3 shown in Fig. 3. A: activity profiles of the subject while performing the cycle task under four experimental conditions at a Ta of 30°C and a RH of 50%. BG: time profiles of the six parameters.
Fig. F1.
Fig. F1.
Scatterplot comparing the estimated Tc against the corresponding measurements across all 166 subjects and experimental conditions (42,026 data points from 247 time profiles). The solid line is the line of equality. The Pearson’s correlation coefficient was 0.72.

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