WO2022250856A1 - Sensing leg movement for wearable monitoring of energy expenditure - Google Patents

Abstract

A wearable system and method are provided for estimating metabolic energy expenditure in real-time during steady-state and time-varying. Using inertial measurement units (IMUs), activities with steps or cycles were performed by a person. Collected data from the IMUs are segmented as one value for each of the steps or cycles. The estimated energy expenditure is estimated by inputting the segmented collected data to a trained model. The trained model is defined to output the estimated energy expenditure for the one value, and was trained mapping the activities segmented inertial data for steps or cycles to energy expenditure as one value for each of the steps or the cycles. The estimated energy expenditure as a function of time is outputted as one value for the step or the cycle for the activities.

Description

SENSING LEG MOVEMENT FOR WEARABLE MONITORING OF

ENERGY EXPENDITURE

FIELD OF THE INVENTION This invention relates to methods and devices for activity monitors, smart watches and heart rate monitors capable of estimating energy expenditure.

BACKGROUND OF THE INVENTION

Physical inactivity is the fourth leading cause of global mortality. Health organizations have requested a tool to objectively measure physical activity, using metrics such as energy expenditure, to relate activity and health outcomes. Respirometry accurately estimates steady- state energy expenditure and doubly labeled water provides weekly estimates, but both are infeasible for everyday use. Smartwatches and wearable estimation methods are portable, but have significant errors. Existing methods estimate poorly during time-varying activities, like short bouts of walking, which comprise 40% of daily steps. Accordingly, there is a need in the art to develop new technology to address the shortcomings in the art. The present invention provides such new technology.

SUMMARY OF THE INVENTION The present invention is a method in which a wearable system estimates metabolic energy expenditure in real-time during steady-state and time-varying activities with substantially lower error than state-of-the-art methods. Experiments were performed to select sensors, collect training data, and validate the wearable system with new subjects and new conditions for walking, running, stair climbing, and biking. It was determined that the wearable system should use inertial measurement units worn on the shank and thigh to measure lower-limb kinematics because they distinguished lower-limb activity better than wrist or trunk kinematics, allowed time-invariant modeling by segmenting strides, and converged more quickly than heart rate or respirometry. The cumulative error of the wearable system’s estimates was 13% across all activities, significantly less than 64% for a heart rate model, 38% for a smartwatch, and 52% for an activity-specific smartwatch. This technology could enable new energy balance systems for weight control or monitoring tools relating activity to outcomes like cardiovascular health.

Embodiments could be developed as smart devices for accurately estimating energy expenditure, or calories burned, during exercise. These smart devices could integrate sensors into the shoe or exercise pants/shorts and make estimates of the energy expended with each step, using a device like a smartphone to provide the information to the user. The unmet need in the art is the ability to accurately estimate the energy people expend throughout their day. This includes many different activities, and can be challenging as people stop and start walking, transition to run, etc. The likely customers would be people interested in better managing their weight as well as athletes that want a better understanding of how much energy they are expending training.

In the embodiments of the smart system, energy expended is estimated during steady-state activities with approximately 12% error, while these smartwatches have an error of 36% to 92%. Thus, embodiments of the present invention offer significantly more accurate monitoring. Prior devices provide estimates at slow, infrequent intervals of every ten seconds to one minute, while embodiments of the present invention provide an estimate once per step. Embodiments of the present invention are the first device to be able to accurately estimate energy expenditure during time-varying activities, for example short bursts of walking and sports such as soccer or basketball where people frequently change speeds between walking and running. Embodiments of the present invention have an error during time-varying conditions of approximately 12% while comparable smartwatches have errors of 80% or greater.

Steps and cycles

Cycles are defined as cyclical motions by when e.g. the shank of the person changes a rotational direction. For example, rotating forward as the person is taking a step and rotating backwards once the foot is on the ground. Same principle applies when cycling but just based on these changes in the cyclic movement.

Steps are defined as the leg movement between subsequent heel strikes of the same leg of the person. A step can also be defined as the leg movement between subsequent heel strikes of the same leg (right heel strike to right heel strike, etc.). In one embodiment, the present invention provides a method of estimating energy expenditure of a person. In this method one would have a first inertial measurement unit on a first body segment (e.g a thigh) of the person, and a second inertial measurement unit on a second body segment (e.g. a shank) of the person. The invention is not limited to the shank and the thigh, and could also be other body segments. In one embodiment, the person performs an activity having steps or cycles. In another embodiment, the person performs at least two of activities selected from a plurality of different activities each having steps or cycles, and each of the plurality of different activities differ from each other in steady-state conditions and time-varying conditions. Examples of activities are walking, running, jumping, cycling, stepping, or the like.

The method continues to collect the data, using a data collection unit, from the first inertial measurement unit and the second inertial measurement unit during the person’s performance. Using a segmentation unit the collected data is segmented as one value for each of the steps or the cycles. The estimated energy expenditure is estimated, using an estimation unit, by inputting the segmented collected data to a trained model, whereby the trained model, preferably stored, is defined to output the estimated energy expenditure for the one value.

In one embodiment, the trained model was trained mapping for activity’s segmented inertial data for steps or cycles performed by a group of people to energy expenditure as one value for each of the steps or the cycles. In another embodiment, the trained model was trained mapping for the plurality of different activities segmented inertial data for steps or cycles of the plurality of different activities performed by a group of people to energy expenditure as one value for each of the steps or the cycles. The method can be extended by having a graphical interface for showing or plotting the estimated energy expenditure as a function of time as one value for the step or the cycle for the one or more activities performed by the person. In the method, cycles are defined as cyclical motions by when the shank of the person changes a rotational direction. In the method, steps are defined as leg movement between subsequent heel strikes of the same leg of the person.

In another embodiment, as a system for estimating energy expenditure of a person, one would have a first inertial measurement unit suitable to be placed on a thigh of the person, and a second inertial measurement unit suitable to be placed on a shank of the person. The data collecting unit, the segmentation unit, the estimation unit, the trained model, and the graphical interface are computer-implemented module integrated as part of the system. BRIEF DESCRIPTION OF THE DRAWINGS

For gray-scale interpretation of the drawings the reader is referred to the priority document which has color drawings of the drawings submitted herewith.

FIGs. 1A-C show according to an exemplary embodiment of the invention the Wearable System components, energy expenditure estimation methods, and experimental conditions. (FIG. 1A) The Wearable System has a microcontroller, battery, and an inertial measurement unit (IMU) attached to the shank and thigh on one leg. (FIG. IB) The Wearable System estimated energy expenditure in real time, using a model trained with data from 13 subjects completing three conditions of walking, running, stair climbing, and biking. The trained model was held constant to test the Wearable System with 24 new subjects during two different steady-state conditions for the same activities and four new time-varying conditions. These subjects had not participated in previous experiments and were selected to emulate a diverse adult population. (FIG. 1C) The Wearable System was compared to commercial devices including the Smartwatch and the

Activity-Specific Smartwatch as well as baselines including the Heart Rate Model, Per-Breath Respirometry, and Fast-Estimated Respirometry.

FIGs. 2A-C show according to an exemplary embodiment of the invention estimating energy expenditure during steady-state conditions. (FIG. 2A) Methods estimating energy expenditure were evaluated during six-minute steady-state conditions followed by three-minutes of quiet standing. Two conditions were collected for each activity in a randomized order. The estimates were interpolated at one second intervals, averaged over subjects, and low-pass filtered. (FIG. 2B) The error as a function of time from the start of the condition evaluated how quickly the methods reached a steady-state estimate, averaged across all conditions. The absolute percent error was computed by taking the mean absolute error between the estimates and ground truth Steady- State Respirometry. (FIG. 2C) The steady-state error represents the mean absolute percent error between the estimates of each method averaged over the last 3 minutes of a condition and Steady-State Respirometry. The box extends from the lower to upper quartile values of the data, with a line at the median and a dot at the mean. The whiskers extend to the last data point within 2.5 times the interquartile range. Per-Breath Respirometry and Fast-Estimated Respirometry were not compared because they become Steady-State Respirometry when averaged over multiple minutes. (FIG. 2D) Cumulative energy expenditure is the total expenditure during each steady-state condition, including expenditure above quiet standing during the three-minutes following the condition. The cumulative error represents the mean absolute percent error between cumulative estimates for each method and Per-Breath Respirometry.

FIGs. 3A-F show according to an exemplary embodiment of the invention estimating energy expenditure during time-varying conditions. The time-varying conditions included periodic profiles of treadmill speeds including (FIG. 3A) discrete steps between quiet standing and walking, (FIG. 3B) sinusoidally- varying walking, (FIG. 3C) discrete steps from walk to run, and (FIG. 3D) sinusoidally-varying walk to run. Interpolated Respirometry approximated ground truth by interpolating between subject-specific Steady-State Respirometry values from walking and running conditions based on treadmill speed. The error profiles represent one standard deviation. (FIG. 3E) The error over time represents the mean absolute percent error between estimates from each method and the Interpolated Respirometry. The box extends from the lower to upper quartile values of the data, with a line at the median and a dot at the mean. The whiskers extend to the last data point within 2.5 times the interquartile range. (FIG. 3F) Cumulative energy expenditure error was computed as the mean absolute percent error between cumulative estimates for each method and Per-Breath Respirometry.

FIGs. 4A-B show according to an exemplary embodiment of the invention interpreting the Wearable System. (FIG. 4A) The Wearable System used a linear regression model to estimate energy expenditure with inputs from inertial measurement units worn on the shank and thigh. The inertial measurement units have a three- axis accelerometer (accel) and a three-axis gyroscope (gyro). The X, Y, and Z directions represent the fore-aft, mediolateral, and vertical axes, respectively. These orientations are assigned during quiet standing, but the sensors are attached to different body parts that move relative to the global reference frame. Input data were low-pass filtered, split by stride, and discretized each stride to a fixed input size before being used in the model. The model used ridge regularization that penalized the sum of the squared model weights. A larger magnitude weight indicated a more informative input. The input signals are shown in descending order of importance based on contribution to total model weight. Gyroscope inputs were more informative than accelerations. Inputs in the second and fifth quintile of each stride were the most informative. (FIG. 4B) The input signal with largest weight, the gyroscope measurement of the shank in the sagittal plane, was plotted for each activity alongside the model weights. The linear regression model may relate the absolute value of signals to energy expenditure or differentiate two points of the input data to approximate a derivative. Interpretation is challenging as all inputs are compared at once

FIG. 5 shows according to an exemplary embodiment of the invention visual illustration of the Data-Driven Model. The Data-Driven Model processes input data by segmenting stride, filtering, discretizing to a fixed input size, and flattening the processed inputs to a vector. An estimate of energy expenditure is computed by passing the processed inputs to a trained linear regression model

FIG. 6 shows according to an exemplary embodiment of the invention a method of estimating energy expenditure of a person. FIG. 7 shows according to an exemplary embodiment of the invention a system for estimating energy expenditure of a person.

DETAILED DESCRIPTION The inventors conceived that using a data-driven method without subject-specific training data that relies on wearable measurements of lower-limb kinematics and segmenting input data by stride would estimate energy expenditure more accurately than state-of-the-art methods during common activities including walking, running, stair climbing, and biking. Lower-limb kinematics provides more information than heart rate, wrist kinematics, or trunk kinematics because lower-limb activities are both more popular for exercise and have larger energy expenditure than upper-limb activities. Lower-limb kinematics converge more quickly than heart rate or respirometry, enabling estimation during time-varying activities. Measuring lower- limb kinematics requires only a few low-cost and wearable inertial measurement units. During these activities, lower-limb kinematics are periodic and can be segmented by stride. This new modeling approach creates time-invariant inputs appropriate for data-driven models such as linear regression which requires minimal computation time. Additional information from percent stride may improve estimation accuracy compared to existing data-driven methods. To evaluate this conception, the inventors performed experiments to select two sensors worn on one leg from a comprehensive set of existing wearable biomechanics sensors. Next, the inventors collected training data and validated a wearable system with a diverse group of new subjects during new steady-state and time-varying conditions. This approach is conceived as part of a novel energy balance system for weight control and a data collection tool relating physical activity to outcomes like cardiovascular health. Evaluating the wearable data-driven method

To monitor physical activity by accurately estimating energy expenditure, the inventors evaluated several methods, explored sensor importance, and extended estimation to time- varying conditions. Energy expenditure during steady-state activities was estimated where each healthy subject (n = 13) participated in one condition of sideways walking, backwards walking, and hopping as well as multiple conditions of normal walking, loaded walking, and running. Ground truth energy expenditure was measured by averaging respirometry measurements from the last three minutes of each condition, which was referred to as Steady-State Respirometry. An initial exploration estimated energy expenditure during time-varying conditions where healthy subjects ( n = 4) transitioned between walking and running with a 30 second period. Ground truth during time-varying conditions was approximated by interpolating between subject- specific Steady-State Respirometry values from walking and running conditions based on treadmill speed, which was referred to as Interpolated Respirometry. The data were recorded with tethered respirometry and wearable sensors including electromyography, force sensing insoles, inertial measurement units, and a heart rate monitor. Metabolic energy expenditure was estimated with several methods including: the Heart Rate Model, the Activity Monitor, the Musculoskeletal Model using muscle-level energy estimates, the Data-Driven Model using all wearable sensor data segmented by stride in a linear regression model (FIG. 5), Per-Breath Respirometry, and Fast-Estimated Respirometry which fit lab-based respirometry measurements to a first-order exponential function for quicker steady-state estimates. Accuracy was evaluated by removing one subject and one condition from the training data, fitting a model to the training data, estimating energy expenditure for the withheld subject and condition, and comparing to ground truth. This was performed for all permutations of subjects and conditions and averaged the error.

It was validated that the Data-Driven Model using all wearable sensor inputs was the best wearable method for estimating energy expenditure because it had the lowest errors during steady-state and time-varying conditions. The Data-Driven Model had 10% relative error during steady-state conditions, about half the error of the second-most accurate model. The Data- Driven Model estimates were constant from the start of the condition because input signals converged quickly, as expected. Fast-Estimated Respirometry had the lowest steady-state error after 74 seconds, confirming its usefulness as a laboratory-based test where accuracy is paramount and longer trial times are acceptable. During time-varying conditions the Data- Driven Model had 7% absolute error, about one-quarter the error of the next-most accurate model. Physiological signals had a delayed response to changing energy expenditure, causing significant error in steady-state and time-varying conditions.

The Data-Driven Model error decreased with additional training data and increased when estimating activities with energy expenditure values significantly different from the training data. Holding out and evaluating conditions besides running resulted in errors between 10% and 15%, indicating some generalization to new conditions. Holding out and evaluating running conditions resulted in the largest errors because the model estimated smaller energy expenditure values similar to the training data. Thus, the similarity of training data impacts the error when estimating new conditions. The approach used by the Data-Driven Model requires training data for all activities that will be monitored. The Musculoskeletal Model was less sensitive to the choice of training data. Combining these two methods may perform best when estimating energy expenditure for many new activities. The inventors focused on estimating known activities and selected the Data-Driven Model because it had greater accuracy and required minimal computation, when provided with sufficient training data.

Selecting informative sensors

The Data-Driven Model was evaluated with different inputs to select an informative set, and an inertial measurement unit on the shank and thigh of one leg were found to have the lowest steady-state error. The inventors first compared inputs from permutations of four sensor classes including: inertial measurements, muscle activity, kinematics, and vertical ground reaction forces. The inventors evaluated these existing sensors rather than develop new sensors to ensure they would be commercially available. The inertial measurement units had the lowest error when using only one sensor class and were selected. Then all permutations of the inertial measurement units were compared, each of which had a triaxial accelerometer and gyroscope. The best results were achieved with one sensor on the shank and one on the thigh. Input from these two sensors had 13.7% relative error, compared to 10% error when using inputs from all sensors. Using a single inertial measurement unit on the thigh resulted in an error of 16.7%, indicating a single sensor such as a smartphone strapped to the leg may not be as accurate. The selected inertial measurement units offered some additional benefits beyond other wearable sensors. They are low-cost, which may enable large-scale use. They are lightweight, compact, easy to don and doff, and allow uninhibited motion. Processing data from these sensors required little computation; a portable microcontroller computed real-time energy expenditure estimates in 0.01 seconds.

Designing and training the Wearable System Next, the Wearable System was built, which has a microcontroller and battery worn on a belt as well as two inertial measurement units worn on the shank and thigh of one leg (FIG. 1A). The total system cost was approximately $100 in retail components. The Wearable System weighed 232 grams and could estimate energy expenditure for 7.3 hours on a single charge. The Wearable System estimated energy expenditure using a new Data-driven Model trained with a combination of previously-collected and new data. The previously-collected walking and running data used to select the best estimation method were combined with a new experiment where healthy subjects climbed stairs and hiked (n = 11) (FIG. IB). The stair climbing conditions were collected on a stairmill at speeds of 40, 60, and 80 steps per minute. The biking conditions were collected on a stationary bike at resistance levels of 20, 70, and 150 Watts while pedaling at 80 revolutions per minute. Pilot tests revealed that changes in the placement of the inertial measurement units resulted in large estimation errors. To address this, random rotations to the sensors were applied in the training data to create synthetic data. The Data-Driven Model was trained with this synthetic data to improve robustness to orientation errors. The Wearable System used this robust model for all evaluations with new subjects and new conditions. Evaluating the Wearable System with new subjects and new conditions

The inventors compared the Wearable System to commercial products and other methods of estimating energy expenditure to determine the estimation error for new subjects and new conditions. The methods compared included the Smartwatch, the Activity-Specific Smartwatch, the Heart Rate Model, the Activity-Specific Model, Per-Breath Respirometry, and Fast- Estimated Respirometry (FIG. 1C). The methods were evaluated with a group of diverse subjects ( n = 24, 15 men and 9 women; age = 34.8 ± 11.6 yr; body mass = 74.3 ± 13.1 kg; height = 1.73 ± 0.07 m; body mass index = 24.9 ± 4.1) that had not participated in previous experiments. The subjects completed two new steady-state conditions at intermediate speeds between the three training conditions collected for each activity, as well as four new time- varying conditions. The steady-state conditions included walking at 1.0 and 1.5 m/s, running at 2.5 and 3.0 m/s, climbing stairs at 50 and 70 steps per minute, and biking with a resistance of 50 and 120 Watts. The ground truth energy expenditure during steady-state conditions was Steady- State Respirometry. The time-varying conditions periodically changed treadmill speed for discrete steps between quiet standing and walking, sinusoidal walking speeds, discrete steps between walking and running, and sinusoidal walking and running speeds. Interpolated Respirometry approximated ground truth during time-varying conditions by interpolating between subject-specific Steady-State Respirometry values from walking and running conditions based on treadmill speed.

The Wearable System used inputs of lower-limb kinematics which converged quickly from the start of steady-state conditions, resulting in consistent and low error estimates (FIG. 2A). The other methods relied on physiological signals which had delayed responses to changing energy expenditure and slowly reached steady-state. The other methods had steady-state errors that varied widely by activity. The Wearable System had the lowest error for the first 44 seconds, after which the laboratory -based, Fast-Estimated Respirometry had the lowest error (FIG. 2B). Although respirometry is not feasible for large-scale monitoring, it offers accurate steady-state estimates for training models. The Heart Rate Model, the Smartwatch, and the Activity-Specific Model rely on physiological signals and have large initial errors which decrease over time, but still result in large steady-state errors.

The Wearable System had the lowest steady-state errors of the wearable methods, closely matching Steady-State Respirometry. The steady-state error of the Wearable System was lower than all other methods (paired /-tests: p < lxlO ⁶). During steady-state conditions the Wearable System had 13% steady-state error, about half the error of the second-most accurate model, the Activity-Specific Smartwatch (FIG. 2C). The steady-state errors for the Smartwatch and the Activity-Specific Smartwatch match those from previous studies. Even the Activity-Specific Model, which used manual labeling during steady-state conditions to achieve perfect activity classification, had higher steady-state error than the Wearable System at 18%. The cumulative energy expenditure error of the Wearable System was 12%, significantly lower than the other methods ranging from 38% to 71% (paired /-tests: p < 2^/ 10 ¹⁴) (FIG. 2D).

The Wearable System accurately estimated energy expenditure during time-varying conditions. The Wearable System captured changes in energy expenditure while the other models had incorrect and delayed estimates (FIGs. 3A-D). The error over time for the Wearable System was 23%, significantly less than the 46% to 105% error for other methods (paired /-tests: p < 3><10⁴) (Fig. 3e). The cumulative energy expenditure error followed a similar trend (paired /-tests: p < 7xl0⁴) (Fig. 3f). Across all steady-state and time-varying conditions the Wearable System had a cumulative energy expenditure error of 13%, significantly less than the 42% to 86% for other methods (paired /-tests: p < 2^/ 10²¹) Also evaluated was a version of the Wearable System using only data from the thigh IMU which had a cumulative error of 19%.

The inventors visualized the linear regression model used by the Wearable System to understand how conditions were differentiated to achieve low error. The magnitude of the model weight assigned to an input indicated importance (FIG. 4A). Larger weights were assigned to the gyroscope inputs. Certain portions of each stride also had larger weights, such as the second and fifth quintiles. The model weighting as a function of percent stride was similar to the standard deviations of input signals across activities. The normalized dot product between the weights and standard deviation of input signals resulted in a cosine similarity of 0.96, indicating the high-dimensional trends were similar. The most informative input signal was plotted alongside the model weights to illustrate how it contributed to an estimate of energy expenditure (FIG. 4B). Interpretation of how inputs contribute to estimates is difficult as all inputs are compared at once.

Subject surveys found the Wearable System to be comfortable and have high usability. 21 subjects who participated in the validation of the Wearable System were surveyed. The usability was evaluated with the System Usability Scale. The Wearable System had a relatively high overall score of 80.9 out 100 averaged across subjects, which is the 90^th percentile among 5,000 device surveys that used the System Usability Scale. The comfort related metrics were evaluated with a survey based on the Questionnaire for User Interaction Satisfaction. The Wearable System had high scores associated with different comfort related attributes. This indicates the Wearable System, which is a research prototype, has potential for use in clinical or at-home settings. Discussion

The approach used in the Wearable System meets the requirements to monitor physical activity on a large scale, thereby providing a tool for managing weight and relating activity to health outcomes. The Wearable System used low-cost inertial measurement units worn on the shank and thigh of one leg to estimate energy expenditure in real-time. This approach is portable and unobtrusive, meeting the criteria to allow for everyday use. It was demonstrated that the Wearable System accurately estimated energy expenditure during steady-state and time-varying activities including walking, running, stair climbing, and biking, the activities that contribute the most to daily energy expenditure. The Wearable System was evaluated with a diverse group of subjects, indicating it may effectively monitor most adults. The Wearable System estimated energy expenditure once per stride, possibly enabling new types of studies such as understanding health benefits from acute dose-response due to repeated, low-intensity exercise. The cumulative energy expenditure error of the Wearable System was one-third the error of state-of-the-art wearable methods, a substantial improvement that could better relate physical activity to health outcomes.

The Activity Monitor had twice the steady-state error of the Data-Driven Model, which may be because it relied on hip kinematics rather than lower-limb kinematics and neglecting stride information. The success of the data-driven approach seems to be largely attributable to the selection of lower-limb kinematics as inputs and segmenting data by stride. A version of the Data-Driven Model using only trunk kinematics as inputs resulted in twice the steady-state error, reinforcing the benefits of using lower-limb kinematics. When the Activity Monitor and Data-driven Model were given the same trunk kinematics as inputs, estimation differences were due to differences in data segmentation. The Data-Driven Model segmented data by stride for time-invariant estimates and achieved lower error than the Activity Monitor, which counted acceleration measurements that reached a threshold. Future devices designed to estimate energy expenditure may benefit from using sensors that measure lower-limb kinematics and models that exploit stride structure.

The Activity-Specific Smartwatch and the Smartwatch had three-fold higher cumulative error than the Wearable System, potentially because of a reliance on heart rate and wrist kinematics rather than lower-limb kinematics. Previous smartwatch studies report similar errors from 35% to 93% when estimating energy expenditure for new subjects, supporting the idea that smartwatches have significant error. The sensor inputs and models used by the smartwatches are not publicly available, but the results indicate the Activity-Specific Smartwatch relies on heart rate and the Smartwatch relies on wrist kinematics. The Activity-Specific Smartwatch exhibited similar trends to the Heart Rate Model, including higher estimates during walking and quiet standing, estimates drifting during conditions, and a delayed response to changes in energy expenditure (FIG. 2A). The Smartwatch estimates during stair climbing and biking were substantially lower than ground truth values, possibly because subjects held onto safety railings which minimized wrist motion. The smartwatches may have higher error because they do not seem to segment data by stride, as indicated by the large initial steady-state error and drift in estimates. The Wearable System had a consistent level of error across all steady-state conditions. Previous experiments found activity monitors to estimate energy expenditure with 30% error for wrist-worn devices and 27% for hip-worn devices, suggesting these locations do not capture motion related to energy expended by lower-limb muscles as accurately as sensors placed on the legs. These results suggest the wrist is a suboptimal placement for sensors when estimating energy expenditure.

The finding that the Wearable System provides significantly more accurate energy expenditure estimates than existing wearable methods by using two carefully selected sensors is surprising. From an information theoretic perspective, one would expect that selecting multiple sensors would achieve at least the same accuracy of a single prescribed sensor, such as a smartwatch. However, the careful selection of two IMU sensors enabled the Wearable System to have three times lower cumulative error than the smartwatches. A version with inputs from the single thigh IMU still had less than half the cumulative error of the smartwatches. Including heart rate, a signal used in many wearable methods for estimating energy expenditure, as an input to the Wearable System did not improve the accuracy. Even using comprehensive sensor measurements of leg kinematics and major muscle groups performed similarly to the two selected IMU sensors. The Wearable System was more accurate than wearable data-driven methods using a variety of sensors and subject-specific training data with errors of 14% to 27%, which would have approximately twice the error when evaluating new subjects. When designing wearable devices, rigorous sensor selection may provide counterintuitive results that can significantly improve performance. The Smartwatches’ large errors were likely due to a reliance on heart rate, rather than a difference in training data. The Smartwatch and Heart Rate Model had similar average steady- state errors of 43% and 39% and match trends across individual conditions. The Heart Rate Model had significantly higher error than the Wearable System, despite being trained with the same data. This suggests that heart rate was less informative than lower-limb kinematics. No information is available about the data used to train the commercial Smartwatch methods. The similarity between the Heart Rate Model and commercial Smartwatch methods indicate they would likely have significantly higher error than the Wearable System, even if trained from the same data. The Wearable System estimates had no statistically significant correlation between error and age, height, weight, or body mass index. The results from evaluating the different methods with a diverse group of subjects suggest the Wearable System would likely be more accurate than the Smartwatch methods when monitoring most adults.

The Wearable System estimated time-varying energy expenditure much more accurately than other methods because it was based on lower-limb kinematics that more closely tracked the activity in the leg muscles which contribute to most of the energy expenditure. The Wearable System estimates were accurate from the start of steady-state conditions (FIG. 2A), captured sinusoidal (FIGs. 3B, 3D) and step (FIGs. 3A, 3C) changes in energy expenditure during time- varying conditions, and had low cumulative error. Lower-limb kinematics are known to quickly converge to steady state following gait changes and track continuous fluctuations in walking speed. The other methods relied on physiological signals which had a delayed response to changing energy expenditure that caused significant error during the start of steady-state conditions, throughout time-varying conditions, and cumulatively (FIGs. 3E, 3F). It was estimated instantaneous energy expenditure during time-varying conditions using measured energy expenditure from steady-state conditions and interpolation based on speed. This assumes the instantaneous energy expenditure matches the work rate of the subject at each instant in time, which was shown to match closely for walking conditions below the aerobic threshold. The time-varying conditions had a period of 30 seconds, faster than the delays in breath-to- breath measurements. The 30 second period was selected to minimize energy expenditure associated with changing speeds with a low average acceleration of 0.07 m/s². Prior experiments found that varying walking speeds by 0.6 meter per second sinusoidally with a 4 second period (0.15 m/s² acceleration) increased the energy expenditure by 4% to 8%. Assuming that increased energy cost is linearly related to acceleration, the cumulative energy expenditure during time- varying conditions would be about 2% to 4% higher than the interpolated estimates of instantaneous energy expenditure, because they interpolate between steady-state energy expenditure which do not include the costs of additional acceleration.

Visualizing the linear regression model used by the Wearable System revealed that gyroscope measurements and percent stride of input data contributed to accurate estimation. The linear regression model had larger weights assigned to gyroscope inputs (FIG. 4A), possibly because angular velocity better captured the motion of two bodies connected by a pin joint. Model weight varied across each stride with large weights during the second and fifth quintiles, indicating knowledge of phase within a stride is important for estimation. Portions of each stride with larger weights also had larger standard deviations in input signals across activities. The model may use phases with large differences to distinguish activities, similar to activity classification. The Wearable System still had lower steady-state error than the Activity-Specific Model even given the fact that the Activity- Specific Model was based on ideal activity classification performed manually. This indicates that the Wearable System may extract additional information such as how the activity was performed, where changes in motion may relate to muscle-level energy expenditure.

Interpreting how the Wearable System estimates energy expenditure from input signals is challenging because all inputs are compared at once. Simple, interpretable mechanisms by which the linear regression model might operate include relating the absolute value of signals to energy expenditure or differentiating two points of the input data to approximate a derivative. To illustrate this, the inventors compared the most informative input signal, the gyroscope measurement of the shank in the sagittal plane, alongside the model weights (FIG. 4B). The 10^th and 11^th points in the stride have a large positive weight and the running input signal has the highest value at these points; the model may directly associate this signal with large energy expenditure during running. The 3^rd and 4^th points in the stride have large weights, one positive and one negative, which may differentiate these two points and distinguish the walking condition, which has a large positive slope, from biking, which has a slope near zero. Segmenting input signals by stride creates 360 parameters to capture information for accurate estimation, but simultaneous comparison of so many inputs makes exact model interpretation impossible. While one cannot say for sure, the model seems to utilize absolute weighting and differentiation to distinguish conditions. The approach used by the Wearable System may be effective for monitoring physical activity, but improved hardware could be desirable for large scale deployment. The Wearable System in one embodiment was a proof-of-concept device with a bulky microcontroller and wired sensors. Despite being a prototype, the subject surveys reported that the Wearable System had a high usability rating and high ratings in metrics rated to comfortability. This is likely due to the light weight and small form factor of the IMUs. A smartphone could provide wireless sensor communication and compute estimates. This future product will also require investigation to determine if it is convenient enough for large scale, everyday use.

The Wearable System accurately estimated energy expenditure for the tested conditions, but additional data collection may improve performance and the activities that can accurately be monitored. The Wearable System was trained with data from 13 young and healthy subjects during four common activities. Collecting data from a larger and more diverse group of subjects and activities would create a more accurate and general model, which may require additional information such as subject age. Additional training data would need to be collected and used to retrain the Wearable System to accurately estimate energy expenditure for any other activities. Early evaluations of other machine learning models performed worse than linear regression, likely because they overfit to the relatively small amount of training data. Future studies with access to more data may benefit from a more expressive model, such as a Neural Network. Activities that have significant upper-limb activity may be challenging to detect without additional sensors but are not among the most common activities with a high energy expenditure and thus may comprise only a small portion of active energy expenditure. Likewise, activities beyond the aerobic threshold are not considered due to the challenges of obtaining ground truth energy expenditure values. Accurately estimating conditions with similar kinematics but different energy expenditures, such as biking at different resistances, may be susceptible to error if people consistently achieved the same kinematics. However, in freely selected behaviors, people tend to have large variations in kinetics and muscle activity. Evaluating other possible signals, such as respiration frequency, may help differentiate energy expenditure for conditions with similar kinematics.

The approach demonstrated by the Wearable System may offer a solution to one of the challenges facing engineers, physicians, and global health organizations: accurately and objectively monitoring common physical activities with a portable, low-cost system. The accuracy when evaluated with a diverse population indicates the Wearable System may be ready to be deployed for effective physical activity monitoring of most adults. The Wearable System relies on two low-cost sensors which may simplify deployment at large scale, especially for low- income countries and countries with high mortality rates from inactivity. Clinical researchers studying obesity and physical activity could use systems like this one to more accurately investigate how activity relates to health outcomes and inform health policies. Engineers designing wearable devices could leverage our sensor selection approach to improve the effectiveness of their devices. Machine learning researchers may find these insights into using gait cycle structure to create time-variant inputs helpful for modeling other challenges related to motion and physiology. Biomechanics researchers may be interested in the implications of the selected sensor signals and locations for monitoring and understanding gait and energy expenditure. The Wearable System could be combined with a method for estimating caloric intake to create an energy balance system. Monitoring and understanding energy balance could enable personalized weight management tools to reduce obesity.

Experimental Design

One of objectives for this invention was to compare error when estimating energy expenditure of the Wearable System method and state-of-the-art wearable methods. It was hypothesized that the Wearable System would have significantly lower error than the state-of-the-art methods. The necessary sample size to validate the Wearable System was found to be 15 subjects from a power analysis based earlier experiments which estimated the Wearable System would have 14% absolute error, a standard deviation of 12%, a difference of at least 14% with each compared method, and a power of 0.9. We stopped data collection after reaching 25 subjects in case of sensor failures and because some subjects were not able to complete all conditions. The experiments included human subject testing in a laboratory experiment, where each subject performed the same set of conditions in a randomized order. Each of the four experiments performed in this study are detailed in the next four sections. These sections each describe the motivation for the experiment, which sensors were used to collect data, and how the data were collected. The subheading for each experiment matches the corresponding subheading in the

Results section. Evaluating the wearable data-driven method and selecting informative sensors

To evaluate the Data-driven method and select the fewest sensors necessary to estimate energy expenditure, the inventors performed an experiment to collect data from a variety of conditions and wearable sensors for offline testing. Healthy young adults (n = 13, 8 men and 5 women; age = 23.8 ± 2.6 yr; body mass = 68.3 ± 10.6 kg; height = 1.72 ± 0.07 m) completed 12 steady-state conditions on a treadmill. The conditions were completed in the order: quiet standing, 6 speeds of walking and running between 0.75 and 3.25 m/s, sideways walking at 1 m/s, backwards walking at 1 m/s, hopping in place at a self-selected rate and height, and loaded walking at 1.25 m/s with an additional 10% and 20% of the subject’s body weight. The conditions lasted 5 minutes followed by quiet standing for at least 1 minute. The minimum, maximum, and average energy expenditures across conditions were 179, 1295, and 471 Watts.

Biomechanics data were collected with a variety of wearable sensors. Tethered respirometry equipment (Quark CPET, COSMED) measured the volume of carbon dioxide and oxygen exchanged per breath. A heart rate monitor (Dual Heart Rate Monitor, Garmin) recorded heart rate in beats per minute at the same intervals as the respirometry measurements, for the last 9 subjects. Electromyography sensors (Trigno IM, Delsys Inc.) recorded muscle activity at 2000 Hz from 7 muscles of the left leg: soleus, medial and lateral gastrocnemii, tibialis anterior, vastus medialis, rectus femoris, and biceps femoris. Inertial measurement units (MTw Awinda, Xsens) recorded motion at 100 Hz from 7 sensors placed on the pelvis and the foot, shank, and thigh of both legs. Force sensing insoles (Pedar, Novel) in both shoes recorded vertical ground reaction forces at 50 Hz. The data processing steps for these sensors are detailed in the “Sensor data processing” subsection. The wearable data were used to compare a variety of methods including: Steady-State Respirometry, Fast-Estimated Respirometry, the Activity Monitor, the Activity-Specific Model, the Data-Driven Model, and the Musculoskeletal Model.

Extending estimation to time-varying conditions

The second experiment collected the same sensor data and steady-state conditions with additional time-varying conditions that periodically transitioned between walking and running. Healthy young adults (n = 4, 2 men and 2 women; age = 23.8 ± 2.6 yr; body mass = 67.1 ± 10.7 kg; height = 1.71 ± 0.07 m) completed the protocol from the first experiment and two time- varying conditions where the speed of walking and running periodically followed a sinusoid or four discrete step changes between 1.25 m/s and 2.75 m/s. The sinusoidal change in speed had a period of 30 seconds. The discrete steps were speeds of 1.25, 1.75, 2.25, and 2.75 m/s. Each discrete step change had a two second acceleration followed by eight seconds of a constant speed, resulting in a total period of 60 seconds. The time-varying conditions started with 10 seconds of walking at 1.25 m/s and then periodically changed the speed for 5 minutes.

The instantaneous energy expenditure during time-varying conditions cannot be directly measured with respirometry due to a delayed response to changing energy expenditure. Interpolated Respirometry approximated ground truth by interpolating between subject-specific Steady-State Respirometry values from walking and running conditions based on treadmill speed. The methods for estimating time-varying energy expenditure included: the Data-Driven Model, the Heart Rate Model, Per-Breath Respirometry, and Fast-Estimated Respirometry.

Designing and training the Wearable System

The third experiment combined a new collection of stair-climbing and biking conditions with previous walking and running data from the first experiment to train the Data-Driven Model used in the Wearable System. Healthy young adults ( n = 10, 5 men and 5 women; age = 24.5 ± 2.5 yr; body mass = 65.5 ± 11.0 kg; height = 1.72 ± 0.07 m) completed three steady-state conditions for both stair climbing and biking. The speeds for stair climbing were 40, 60, and 80 steps per minute which were selected to center around the speed for healthy older adults. A stairmill was used to emulate continuously climbing stairs while remaining in one location for data recording. The kinematics and muscle activity for climbing stairs and using a stairmill follow similar trends. The biking conditions had resistance levels of approximately 20, 70, and 150 Watts. The subject manually followed a pedal rate of 80 revolutions per minute based on findings that this is a comfortable rate.

The Wearable System was assembled from a few off-the-shelf components and estimated energy expenditure in real-time with the Data-Driven Model trained from experimental data. The Wearable System has a Raspberry Pi 3b+, a rechargeable battery, and two Adafruit Precision NXP Breakout Boards. Computation and data storage were performed on the Raspberry Pi in real-time. The Data-Driven Model relied on inputs from the two inertial measurement units worn on the shank and thigh of the left leg. The Wearable System identified quiet standing when strides were not detected for at least 8 seconds and used a heuristic to estimate energy expenditure. If a stride was not detected for 8 seconds the Wearable System switched to estimate quiet standing from a scaled estimate of basal energy expenditure. An equation was used to estimate basal energy expenditure from a subject’s height, weight, age, and gender. The scaling factor was computed dividing Steady- State Respirometry estimates during quiet standing by basal estimates and averaging across all training subjects. When evaluating the energy expenditure during quiet standing for a new subject, their basal estimate was multiplied by this scaling factor.

Evaluating the Wearable System with new subjects and new conditions The fourth experiment compared the Wearable System and state-of-the-art wearable methods when estimating energy expenditure for new subjects and new steady-state conditions during walking, running, stair climbing, and biking as well as four time-varying activities. The subjects were a diverse group of adults that had not participated in any previous experiments ( n = 24, 15 men and 9 women; age = 34.8 ± 11.6 yr; body mass = 74.3 ± 13.1 kg; height = 1.73 ± 0.07 m; body mass index = 24.9 ± 4.1). The inventors selected participants to achieve similar mean and standard deviation values of the age, body mass, height, and body mass index of a diverse study validating the error of smartwatches estimating energy expenditure. The subjects could skip any conditions they were unable to complete. The new conditions were selected at intermediate speeds or resistance levels between the conditions collected to train the Wearable System. The steady-state conditions included walking at 1.0 (n = 24) and 1.5 (n = 24) m/s, running at 2.5 (// = 13) and 3.0 (n = 11) m/s, climbing stairs at 50 ( n = 22) and 70 {n = 14) steps per minute, and biking with a resistance of 50 {n = 24) and 120 (// = 24) Watts while pedaling at 80 revolutions per minute. The n-values represent the number of the 24 subjects that completed each condition. The time-varying conditions have periodic profiles of varying treadmill speeds including discrete steps between quiet standing and walking at 1.0 m/s, sinusoidally-varying walking speed between 1.0 and 1.5 m/s, discrete steps from walking at 1.0 m/s to running at 3.0 m/s, and sinusoidally-varying from walking at 1.0 m/s to running at 3.0 m/s. Each condition lasted 6 minutes followed by at least 3 minutes of quiet standing. The conditions were collected in two sections, one included walking and running conditions and the other of stair climbing and biking because the cart containing the respirometry equipment had to be moved to reach the exercise equipment. The order of the two sections and the order of the conditions within each section were randomized. The evaluated methods included: the Wearable System, the Smartwatch, the Activity-Specific Smartwatch, the Heart Rate Model, Per-Breath Respirometry, Fast-Estimated Respirometry, and Steady-State Respirometry.

A post-hoc survey of 21 subjects was used to evaluate the usability of the Wearable System as well as metrics related to comfort. The usability questionnaire was the standard System Usability Scale, which is a Likert scale meant to evaluate the usability of a system. 21 participants evaluated the Wearable System with this survey. The metrics related to comfort were based on the Questionnaire for User Interaction Satisfaction survey. Sensor data processing

Wearable sensor data from the first two experiments were processed before being input to any models. Electromyography signals were filtered with a 30 to 500 Hz bandpass filter, rectified, filtered with a 6 Hz low-pass filter, and normalized by the maximum signal for each muscle during walking at 1.25 m/s. The filters were fourth-order, bidirectional Butterworth filters. Some measurements from the force sensing insoles reported negative forces, which were corrected by replacing these values with the first preceding non-negative measurement. The force measurements also drifted over time and were corrected by shifting the minimum value of each ten second window of data to 0, approximating having no vertical ground reaction force during the flight phase of each stride.

The sagittal kinematics for the ankle, knee, and hip angles were computed by passing orientation data from the inertial measurement units to OpenSense, an open-source tool relying on OpenSim musculoskeletal simulation. The OpenSense assumed the subject was standing to calibrate a human musculoskeletal model. The inertial measurement units provided data to an inverse kinematics solver to estimate the lower-limb kinematics while meeting musculoskeletal constraints. The initial calibration and solver were reset for each condition to limit error accumulated from sensor drift. The computed joint kinematics from OpenSense were compared to those from a motion capture system (Optitrack), resulting in an absolute error of 5 degrees averaged across all sagittal joints and conditions.

Sensor data were synced with timestamps from each device and segmented by stride. The first two experiments resampled all sensor data to 100 Hz and segmented strides by detecting when the pressure insole of the right foot reported in increasing force that crossed a threshold of 150

N. The Wearable System filtered and processed inertial measurement data and used sagittal plane measurements to segment strides. This segmentation process is based on the change in angular rotation of the shank of the leg, emulating heel strike during walking and running as well as segmenting any cyclic activity, including biking. The sagittal plane angular velocity of the inertial measurement unit worn on the shank of the left leg was filtered with a fourth-order 6 Hz low-pass filter before detecting peaks. The largest relative peaks were required to be at least

O.5 seconds apart to identify one gait cycle.

The Apple smartwatch data were stored on their paired smartphone and exported from the Health app. The data was split into files containing active energy burned, basal energy burned, and a variety of other information. Each estimate of energy expenditure contained a start and stop timestamp along with a value for kilocalories expended during that period. The energy expenditure rate in Watts was computed by dividing the kilocalories by the duration of time in seconds, and then multiplying by a scaling factor to convert the units to Watts. The active and basal energy estimates were interpolated and then summed to produce total energy expenditure estimates at one second intervals. Estimation methods

The methods of estimating energy expenditure we compared included: Steady- State Respirometry, Per-Breath Respirometry, Fast-Estimated Respirometry, the Activity Monitor, the Activity-Specific Model, the Data-Driven Model, the Musculoskeletal Model, the Smartwatch, and the Activity- Specific Smartwatch. These methods are capable of estimating energy expenditure for extended periods if the activity is within the aerobic threshold. Directly measuring instantaneous energy expenditure of the whole body is not possible. Respirometry cannot measure instantaneous energy expenditure because of significant delays in replenishing energy stored in the muscles, primarily due to mitochondrial dynamics, oxygen consumption, and blood circulation. Activities outside the aerobic threshold violate steady-state assumptions in these respirometry methods and thus cannot be monitored accurately.

Steady- State Respirometry acted as the ground truth energy expenditure values for the steady- state conditions by averaging the last several minutes of respirometry data converted to energy expenditure with the Brockway equation. Conditions collected in the first three experiments lasted 5 minutes and the steady-state estimate was averaged over the last two minutes. Conditions collected in the last experiment to validate the Wearable System lasted 6 minutes and the steady-state estimate was averaged over the last three minutes. Per-Breath Respirometry provided noisier estimates of energy expenditure once per breath also using the Brockway equation. Fast-Estimated Respirometry estimated steady-state quickly by fitting estimates per breath to a first-order exponential function. The asymptote value was treated as the estimate. Time-varying conditions typically do not have a known step change in energy expenditure, limiting use to steady-state conditions.

The Heart Rate Model estimated energy expenditure by using a linear regression model to estimate Steady-State Respirometry from steady-state heart rate values in beats per minute. The linear regression model had one weight and one bias parameter.

The Activity Monitor used a linear model to estimate energy expenditure based on the number of acceleration measurements that reached a threshold every minute. The threshold and count protocol followed the popular ActiGraph procedure. The accelerometer measured three axes and used the processing steps of the triaxial GT3X activity monitor. A regression equation was selected to scale the number of counts to energy expenditure in metabolic equivalents (METs) which had units of kilocalories per kilogram per hour and were converted to Watts for comparison. The Data-Driven Model used wearable sensor data to estimate energy expenditure once per stride. The model was fit using linear regression with ridge regularization with default regularization value of 1. Each stride of data was discretized to a fixed input size by splitting input signals into 30 bins. The discretized input signals were flattened into a vector with single features including the subject’s height, weight, and duration of each stride in seconds. The last 50 strides from each training condition were included in the training data. The training data was standardized separately across each input signal by subtracting the mean and dividing by the standard deviation. Tested conditions were normalized by using the mean and standard deviation from the training data. Interaction and nonlinear terms were not included due to the large number of input signals.

The Activity-Specific Model relied on ideal activity classification to estimate energy expenditure with separate models for each activity. Inputs to the models was subjects’ height, weight, and stride duration. The models were linear regression with ridge regularization, using the default regularization parameter of 1. Although this method was compared to the Wearable System it was evaluated offline to add ideal activity classification.

The Musculoskeletal Model estimated energy expenditure by using a simulated anatomical model tracking measured kinematics and applying measured muscle activity to compute the metabolic rate of each leg muscle. Due to large computation times, estimates were computed from five strides per condition. The anatomical model was scaled by the subject’s height and weight. The measured electromyography data were scaled to muscle activations using activation values from similar running conditions. Scaling to muscle activations during walking resulted in impossible activations above 100% during running (20, 57). Muscle parameters were computed using muscle-driven forward simulation relying on OpenSim software. The normalized fiber length and velocity parameters were validated by comparing to related simulation work. The metabolic rate of each muscle was computed by passing the muscle activations and simulated muscle parameters to a metabolic probe model. This simulation was determined to meet best practices as the simulated net joint moments for the ankle and knee in the sagittal plane were within two standard deviations of experimental data during walking.

The Smartwatch estimated energy expenditure approximately every minute using an undisclosed model provided by Apple. The Smartwatch was an Apple watch series 1 (42mm) with model number A1154 and software version 4.3.2. The inventors evaluated the Apple watch series 1 because it is the only model that has been previously validated in other research experiments. Apple does not provide information whether their method for estimating energy expenditure is different for the generations of smartwatches. However, all versions of their smartwatches have the same set of sensors and utilize the same software application, which we updated to the most recent available version. The estimates were exported from the Health app on a paired iPhone 6S with model number A1633 and operating system version 13.2.3. The inputs to the model are unknown but may include wrist kinematics and heart rate. The Smartwatch was worn on the right wrist and calibrated following Apple’s guidelines. The calibration process for each subject included resetting the calibration, entering subject-specific information in the Health app, and ensuring a snug fit around the wrist. After all data was collected, the estimates were exported from the Apple Health app on the paired smartphone. The Activity-Specific Smartwatch estimated energy expenditure approximately every 3 seconds using undisclosed and Activity- Specific models provided by Apple. The Activity-Specific Smartwatch was an Apple watch series 1 (42mm) with model number A1154 and software version 4.3.2. The estimates were exported from the Health app on a paired iPhone 6 with model number A1549 and operating system version 12.4.4. The Activity-Specific Smartwatch was worn on the left wrist. Before the start of each condition the user selected the appropriate model for that activity. The models for the walking, running, stair climbing, and biking activities were labeled as indoor walk, indoor run, stair stepper, and indoor cycling. The indoor run mode was selected for time-varying activities that included both walking and running. Performance metrics

Absolute error measured the error between estimated and ground truth energy expenditure. The absolute error was calculated by finding the percent error between the estimate and ground truth, taking the absolute value of these errors, and then averaging all errors in each condition.

The relative error metric evaluated model precision in capturing the relative changes in energy expenditure across all conditions. The relative error first removed the difference between estimates and ground truth energy expenditure across all conditions for each subject, eliminating any consistent offset. The relative error was then calculated following the same steps as the absolute error.

The cumulative energy expenditure was calculated as the average energy expenditure over the last 3 minutes of the 6-minute condition, including any expenditure above quiet standing for 3 minutes following the condition. The cumulative energy expenditure approximated the total energy spent during the activity because methods relying on respirometry or heart rate had delayed response in the energy expenditure estimates and remained elevated for several minutes after a condition. The error of cumulative energy expenditure was computed between the estimates and ground truth following the same steps as the absolute error. Statistical Analysis

The method used to estimate energy expenditure had a significant effect for all reported error metrics with a Kruskal-Wallis one-way ANOVA (fixed effect: method; p < 3 ^c 10⁷). The Kruskal-Wallis test was selected because the errors did not follow a normal distribution. The inventors then used paired /-tests to evaluate the significance of the reported errors. The /-test results were compared using a significance level of 0.05 and applied the Bonferroni correction with 15 comparisons, giving a modified significance level of 0.0033. The largest reported value was p = 7x1 O ⁴, indicating all results were statistically significant. There was no significant difference (paired /-test; p = 0.64) in the steady-state absolute error based on gender. Linear regression models that used the subject’s heights, weights, or body mass index to estimate steady-state absolute error resulted in R-squared values of 0.009, 0.024, and 0.017, respectively. Thus, there was no significant correlation between the error and the subject’s height, weight, or body mass index.

Priority

This application claims the benefit of US Provisional Application 63/192460 filed May 24, 2021 which is hereby incorporated by reference in its entirety.

Claims

CLAIMS What is claimed is:

1. A method of estimating energy expenditure of a person, comprising:

(a) having a first inertial measurement unit on a first segment of the person;

(b) having a second inertial measurement unit on a second segment of the person;

(d) the person performing either: (i) an activity, wherein the activity comprising steps or cycles, or (ii) at least two of activities selected from a plurality of different activities each comprising steps or cycles, and wherein each of the plurality of different activities differ from each other in steady-state conditions and time-varying conditions;

(e) collecting data from the first inertial measurement unit and the second inertial measurement unit during the person’s performance;

(f) segmenting the collected data as one value for each of the steps or the cycles; and

(f) estimating the estimated energy expenditure using the segmented collected data as input to a trained model, wherein the trained model outputs the estimated energy expenditure for the one value, and wherein the trained model for (i) was trained mapping for the activity’s segmented inertial data for steps or cycles performed by a group of people to energy expenditure as one value for each of the steps or the cycles, or wherein the trained model for (ii) was trained mapping for the plurality of different activities segmented inertial data for steps or cycles of the plurality of different activities performed by a group of people to energy expenditure as one value for each of the steps or the cycles.

2 The method as set forth in claim 1, wherein for (i) the estimated energy expenditure is plotted as a function of time as one value for the step or the cycle for the activity, or wherein for (ii) the estimated energy expenditure is plotted as a function of time as one value for the step or the cycle for the at least two of the activities of a plurality of different activities performed by the person.

3. The method as set forth in claim 1, wherein the cycles are defined as cyclical motions by when the shank of the person changes a rotational direction.

4. The method as set forth in claim 1, wherein the steps are defined as leg movement between subsequent heel strikes of the same leg of the person.

5. A system for estimating energy expenditure of a person, comprising:

(a) a first inertial measurement unit suitable to be placed on first segment of the person;

(b) a second inertial measurement unit suitable to be placed on second segment of the person;

(c) a data collecting unit for collecting data from the first inertial measurement unit and the second inertial measurement unit during a person’s performance, wherein the person’s performance comprises either: (i) an activity, wherein the activity comprising steps or cycles, or (ii) at least two of activities selected from a plurality of different activities each comprising steps or cycles, and wherein each of the plurality of different activities differ from each other in steady-state conditions and time- varying conditions; (d) a segmentation unit for segmenting the collected data as one value for each of the steps or the cycles; and

(e) an estimation unit for estimating the estimated energy expenditure using the segmented collected data as input to a stored trained model, wherein the stored trained model outputs the estimated energy expenditure for the one value, and wherein the trained model for (i) was trained mapping for the activity’s segmented inertial data for steps or cycles performed by a group of people to energy expenditure as one value for each of the steps or the cycles, or wherein the trained model for (ii) was trained mapping for the plurality of different activities segmented inertial data for steps or cycles of the plurality of different activities performed by a group of people to energy expenditure as one value for each of the steps or the cycles.

6 The system as set forth in claim 5, further comprising a graphical interface for showing for (i) the estimated energy expenditure plotted as a function of time as one value for the step or the cycle for the activity, or for (ii) the estimated energy expenditure plotted as a function of time as one value for the step or the cycle for the at least two of the activities of a plurality of different activities performed by the person.

7. The system as set forth in claim 5, wherein the cycles are defined as cyclical motions by when the shank of the person changes a rotational direction. 8 The system as set forth in claim 5, wherein the steps are defined as leg movement between subsequent heel strikes of the same leg of the person.