Estimation of metabolic energy expenditure from core temperature using a human thermoregulatory model.

Human metabolic energy expenditure is critical to many scientific disciplines but can only be measured using expensive and/or restrictive equipment. The aim of this work is to determine whether the SCENARIO thermoregulatory model can be adapted to estimate metabolic rate (M) from core body temperature (TC). To validate this method of M estimation, data were collected from fifteen test volunteers (age = 23 ± 3yr, height = 1.73 ± 0.07m, mass = 68.6 ± 8.7kg, body fat = 16.7 ± 7.3%; mean ± SD) who wore long sleeved nylon jackets and pants (Itot,clo = 1.22, Im = 0.41) during treadmill exercise tasks (32 trials; 7.8 ± 0.5km in 1h; air temp. = 22°C, 50% RH, wind speed = 0.35ms-1). Core body temperatures were recorded by ingested thermometer pill and M data were measured via whole room indirect calorimetry. Metabolic rate was estimated for 5min epochs in a two-step process. First, for a given epoch, a range of M values were input to the SCENARIO model and a corresponding range of TC values were output. Second, the output TC range value with the lowest absolute error relative to the observed TC for the given epoch was identified and its corresponding M range input was selected as the estimated M for that epoch. This process was then repeated for each subsequent remaining epoch. Root mean square error (RMSE), mean absolute error (MAE), and bias between observed and estimated M were 186W, 130 ± 174W, and 33 ± 183W, respectively. The RMSE for total energy expenditure by exercise period was 0.30 MJ. These results indicate that the SCENARIO model is useful for estimating M from TC when measurement is otherwise impractical.

A robust method to estimate instantaneous heart rate from noisy electrocardiogram waveforms.

We propose a new algorithm for real-time estimation of instantaneous heart rate (HR) from noise-laden electrocardiogram (ECG) waveforms typical of unstructured, ambulatory field environments. The estimation of HR from ECG waveforms is an indirect measurement problem that requires differencing, which invariably amplifies high-frequency noise. We circumvented noise amplification by considering the estimation of HR as the solution of a weighted regularized least squares problem, which, in addition, directly provided analytically based confidence intervals (CIs) for the estimated HRs. To evaluate the performance of the proposed algorithm, we applied it to simulated data and to noise-laden ECG records that were collected during helicopter transport of trauma-injured patients to a trauma center. We compared the proposed algorithm with HR estimates produced by a widely used vital-sign travel monitor and a standard HR estimation technique, followed by postprocessing with Kalman filtering or spline smoothing. The simulation results indicated that our algorithm consistently produced more accurate HR estimates, with estimation errors as much as 67% smaller than those attained by the postprocessing methods, while the results with the field-collected data showed that the proposed algorithm produced much smoother and reliable HR estimates than those obtained by the vital-sign monitor. Moreover, the obtained CIs reflected the amount of noise in the ECG recording and could be used to statistically quantify uncertainties in the HR estimates. We conclude that the proposed method is robust to different types of noise and is particularly suitable for use in ambulatory environments where data quality is notoriously poor.

The importance of different frequency bands in predicting subcutaneous glucose concentration in type 1 diabetic patients.

We investigated the relative importance and predictive power of different frequency bands of subcutaneous glucose signals for the short-term (0-50 min) forecasting of glucose concentrations in type 1 diabetic patients with data-driven autoregressive (AR) models. The study data consisted of minute-by-minute glucose signals collected from nine deidentified patients over a five-day period using continuous glucose monitoring devices. AR models were developed using single and pairwise combinations of frequency bands of the glucose signal and compared with a reference model including all bands. The results suggest that: for open-loop applications, there is no need to explicitly represent exogenous inputs, such as meals and insulin intake, in AR models; models based on a single-frequency band, with periods between 60-120 min and 150-500 min, yield good predictive power (error <3 mg/dL) for prediction horizons of up to 25 min; models based on pairs of bands produce predictions that are indistinguishable from those of the reference model as long as the 60-120 min period band is included; and AR models can be developed on signals of short length (approximately 300 min), i.e., ignoring long circadian rhythms, without any detriment in prediction accuracy. Together, these findings provide insights into efficient development of more effective and parsimonious data-driven models for short-term prediction of glucose concentrations in diabetic patients.

A real-time algorithm for predicting core temperature in humans.

In this paper, we present a real-time implementation of a previously developed offline algorithm for predicting core temperature in humans. The real-time algorithm uses a zero-phase Butterworth digital filter to smooth the data and an autoregressive (AR) model to predict core temperature. The performance of the algorithm is assessed in terms of its prediction accuracy, quantified by the root mean squared error (RMSE), and in terms of prediction uncertainty, quantified by statistically based prediction intervals (PIs). To evaluate the performance of the algorithm, we simulated real-time implementation using core-temperature data collected during two different field studies, involving ten different individuals. One of the studies includes a case of heat illness suffered by one of the participants. The results indicate that although the real-time predictions yielded RMSEs that are larger than those of the offline algorithm, the real-time algorithm does produce sufficiently accurate predictions for practically meaningful prediction horizons (approximately 20 min). The algorithm reached alert (39 degrees C) and alarm (39.5 degrees C) thresholds for the heat-ill individual but did not even attain the alert threshold for the other individuals, demonstrating the algorithm's good sensitivity and specificity. The PIs reflected, in an intuitively expected manner, the uncertainty associated with real-time forecast as a function of prediction horizon and core-temperature variability. The results also corroborate the feasibility of "universal" AR models, where an offline-developed model based on one individual's data could be used to predict any other individual in real time. We conclude that the real-time implementation of the algorithm confirms the attributes observed in the offline version and, hence, could be considered as a warning tool for impending heat illnesses.

Universal glucose models for predicting subcutaneous glucose concentration in humans.

This paper tests the hypothesis that a "universal," data-driven model can be developed based on glucose data from one diabetic subject, and subsequently applied to predict subcutaneous glucose concentrations of other subjects, even of those with different types of diabetes. We employed three separate studies, each utilizing a different continuous glucose monitoring (CGM) device, to verify the model's universality. Two out of the three studies involved subjects with type 1 diabetes and the other one with type 2 diabetes. We first filtered the subcutaneous glucose concentration data by imposing constraints on their rate of change. Then, using the filtered data, we developed data-driven autoregressive models of order 30, and used them to make short-term, 30-min-ahead glucose-concentration predictions. We used same-subject model predictions as a reference for comparisons against cross-subject and cross-study model predictions, which were evaluated using the root-mean-squared error (RMSE) and Clarke error grid analysis (EGA). We found that, for each studied subject, the average cross-subject and cross-study RMSEs of the predictions were small and indistinguishable from those obtained with the same-subject models. These observations were corroborated by EGA, where better than 99.0% of the paired sensor-predicted glucose concentrations lay in the clinically acceptable zone A. In addition, the predictive capability of the models was found not to be affected by diabetes type, subject age, CGM device, and interindividual differences. We conclude that it is feasible to develop universal glucose models that allow for clinical use of predictive algorithms and CGM devices for proactive therapy of diabetic patients.

An improved methodology for individualized performance prediction of sleep-deprived individuals with the two-process model.

We present a method based on the two-process model of sleep regulation for developing individualized biomathematical models that predict performance impairment for individuals subjected to total sleep loss. This new method advances our previous work in two important ways. First, it enables model customization to start as soon as the first performance measurement from an individual becomes available. This was achieved by optimally combining the performance information obtained from the individual's performance measurements with a priori performance information using a Bayesian framework, while retaining the strategy of transforming the nonlinear optimization problem of finding the optimal estimates of the two-process model parameters into a series of linear optimization problems. Second, by taking advantage of the linear representation of the two-process model, this new method enables the analytical computation of statistically based measures of reliability for the model predictions in the form of prediction intervals. Two distinct data sets were used to evaluate the proposed method. Results using simulated data with superimposed white Gaussian noise showed that the new method yielded 50% to 90% improvement in parameter-estimate accuracy over the previous method. Moreover, the accuracy of the analytically computed prediction intervals was validated through Monte Carlo simulations. Results for subjects representing three sleep-loss phenotypes who participated in a laboratory study (82 h of total sleep loss) indicated that the proposed method yielded individualized predictions that were up to 43% more accurate than group-average prediction models and, on average, 10% more accurate than individualized predictions based on our previous method.

Predicting subcutaneous glucose concentration in humans: data-driven glucose modeling.

The combination of predictive data-driven models with frequent glucose measurements may provide for an early warning of impending glucose excursions and proactive regulatory interventions for diabetes patients. However, from a modeling perspective, before the benefits of such a strategy can be attained, we must first be able to quantitatively characterize the behavior of the model coefficients as well as the model predictions as a function of prediction horizon. We need to determine if the model coefficients reflect viable physiologic dependencies of the individual glycemic measurements and whether the model is stable with respect to small changes in noise levels, leading to accurate near-future predictions with negligible time lag. We assessed the behavior of linear autoregressive data-driven models developed under three possible modeling scenarios, using continuous glucose measurements of nine subjects collected on a minute-by-minute basis for approximately 5 days. Simulation results indicated that stable and accurate models for near-future glycemic predictions (< 60 min) with clinically acceptable time lags are attained only when the raw glucose measurements are smoothed and the model coefficients are regularized. This study provides a starting point for further needed investigations before real-time deployment can be considered.

Individualized short-term core temperature prediction in humans using biomathematical models.

This study compares and contrasts the ability of three different mathematical modeling techniques to predict individual-specific body core temperature variations during physical activity. The techniques include a first-principles, physiology-based (SCENARIO) model, a purely data-driven model, and a hybrid model that combines first-principles and data-driven components to provide an early, short-term (20-30 min ahead) warning of an impending heat injury. Their performance is investigated using two distinct datasets, a Field study and a Laboratory study. The results indicate that, for up to a 30 min prediction horizon, the purely data-driven model is the most accurate technique, followed by the hybrid. For this prediction horizon, the first-principles SCENARIO model produces root mean square prediction errors that are twice as large as those obtained with the other two techniques. Another important finding is that, if properly regularized and developed with representative data, data-driven and hybrid models can be made "portable" from individual to individual and across studies, thus significantly reducing the need for collecting developmental data and constructing and tuning individual-specific models.

Individualized performance prediction of sleep-deprived individuals with the two-process model.

We present a new method for developing individualized biomathematical models that predict performance impairment for individuals restricted to total sleep loss. The underlying formulation is based on the two-process model of sleep regulation, which has been extensively used to develop group-average models. However, in the proposed method, the parameters of the two-process model are systematically adjusted to account for an individual's uncertain initial state and unknown trait characteristics, resulting in individual-specific performance prediction models. The method establishes the initial estimates of the model parameters using a set of past performance observations, after which the parameters are adjusted as each new observation becomes available. Moreover, by transforming the nonlinear optimization problem of finding the best estimates of the two-process model parameters into a set of linear optimization problems, the proposed method yields unique parameter estimates. Two distinct data sets are used to evaluate the proposed method. Results of simulated data (with superimposed noise) show that the model parameters asymptotically converge to their true values and the model prediction accuracy improves as the number of performance observations increases and the amount of noise in the data decreases. Results of a laboratory study (82 h of total sleep loss), for three sleep-loss phenotypes, suggest that individualized models are consistently more accurate than group-average models, yielding as much as a threefold reduction in prediction errors. In addition, we show that the two-process model of sleep regulation is capable of representing performance data only when the proposed individualized model is used.

Providing statistical measures of reliability for body core temperature predictions.

This paper describes the use of a data-driven autoregressive integrated moving average model to predict body core temperature in humans during physical activity. We also propose a bootstrap technique to provide a measure of reliability of such predictions in the form of prediction intervals. We investigate the model's predictive capabilities and associated reliability using two distinct datasets, both obtained in the field under different environmental conditions. One dataset is used to develop the model, and the other one, containing an example of heat illness, is used to test the model. We demonstrate that accurate and reliable predictions of an extreme core temperature value of 39.5 degrees C, can be made 20 minutes ahead of time, even when the predictive model is developed on a different individual having core temperatures within healthy physiological limits. This result suggests that data-driven models can be made portable across different core temperature levels and across different individuals. Also, we show that the bootstrap prediction intervals cover the actual core temperature, and that they exhibit intuitively expected behavior as a function of the prediction horizon and the core temperature variability.

Machine learning approach to color constancy.

A number of machine learning (ML) techniques have recently been proposed to solve color constancy problem in computer vision. Neural networks (NNs) and support vector regression (SVR) in particular, have been shown to outperform many traditional color constancy algorithms. However, neither neural networks nor SVR were compared to simpler regression tools in those studies. In this article, we present results obtained with a linear technique known as ridge regression (RR) and show that it performs better than NNs, SVR, and gray world (GW) algorithm on the same dataset. We also perform uncertainty analysis for NNs, SVR, and RR using bootstrapping and show that ridge regression and SVR are more consistent than neural networks. The shorter training time and single parameter optimization of the proposed approach provides a potential scope for real time video tracking application.