WO2020074881A1 - Estimation de la fréquence cardiaque au repos - Google Patents

Estimation de la fréquence cardiaque au repos Download PDF

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Publication number
WO2020074881A1
WO2020074881A1 PCT/GB2019/052849 GB2019052849W WO2020074881A1 WO 2020074881 A1 WO2020074881 A1 WO 2020074881A1 GB 2019052849 W GB2019052849 W GB 2019052849W WO 2020074881 A1 WO2020074881 A1 WO 2020074881A1
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WIPO (PCT)
Prior art keywords
heart rate
data
user
base pattern
day
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PCT/GB2019/052849
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English (en)
Inventor
Bartoloni LEONARDO
Morelli DAVIDE
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Biobeats Group Ltd
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Priority claimed from GBGB1816388.1A external-priority patent/GB201816388D0/en
Priority claimed from GBGB1902761.4A external-priority patent/GB201902761D0/en
Application filed by Biobeats Group Ltd filed Critical Biobeats Group Ltd
Publication of WO2020074881A1 publication Critical patent/WO2020074881A1/fr

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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/02—Detecting, measuring or recording pulse, heart rate, blood pressure or blood flow; Combined pulse/heart-rate/blood pressure determination; Evaluating a cardiovascular condition not otherwise provided for, e.g. using combinations of techniques provided for in this group with electrocardiography or electroauscultation; Heart catheters for measuring blood pressure
    • A61B5/024—Detecting, measuring or recording pulse rate or heart rate
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235—Details of waveform analysis
    • A61B5/7246—Details of waveform analysis using correlation, e.g. template matching or determination of similarity
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235—Details of waveform analysis
    • A61B5/7253—Details of waveform analysis characterised by using transforms

Definitions

  • the field of the invention relates to the estimation of a resting heart rate.
  • Heartbeat There are an increasing number of devices being used to monitor things such as an individual’s heartbeat. Various information can be derived from these measurements that may be of interest to a user. For example, changes in heart rate can be used to determine various things such as how hard a user is working when exercising and the number of calories burnt. However, different users have different physiology and thus, such calculations should be tailored to the user.
  • One factor that is important in these estimations is the user’s usual resting heart beat, however, it is not straightforward to accurately measure this.
  • a user’s resting heart rate will vary depending on the time of day and the activity levels of the user and thus, determining an average resting heart rate that accurately characterises a user can be difficult.
  • a first aspect provides a method of determining a user’s resting heart rate, comprising: receiving data indicative of a user’s heart rate sensed over a period of time; fitting at least some of said sensed data to a base pattern indicative of estimated variations in an average person’s resting heart rate over a predetermined time period, said base pattern comprising a cosinor comprising a plurality of harmonics; and determining said resting heart rate from said sensed data fitted to said base pattern.
  • a user’s heart rate is affected by many things such as activity level, mood, stress, eating and sleep.
  • a user’s resting heart rate provides information regarding their fitness and also serves as a base line against which any increase in heart rate due to other factors can be measured.
  • determining a resting heart rate is not straightforward and may be mathematically complex and computationally expensive.
  • the first aspect of the present invention addresses these issues by fitting data indicative of a user’s heart rate to a base pattern that provides a pattern indicative of estimated variations in an average person’s resting heart rate.
  • This base pattern is formed from a cosinor with a plurality of harmonics.
  • a person’s resting heart rate will vary over a period of time and this variation may be periodic to some degree in its nature, as users sleep, work and eat at similarly spaced points in a day.
  • modelling the variations in the resting heart rate using a cosinor with multiple harmonics and fitting measured heart rate to a base pattern modelled in this way is mathematically efficient while providing a useful representation of how heart rate generally varies.
  • a method of determining a resting heart rate that is efficient in processing power and provides an effective output is provided.
  • the resting heart rate is the heart rate where data while active is filtered out.
  • the actual heart rate is the variable that is measured and the resting heart rate is estimated from this.
  • the method further comprises sensing the heart beat and receiving the heart beat data from the sensor, while in other embodiments the step of receiving comprises receiving the data from a remote sensor.
  • the predetermined time period over which the measurements are analysed may be a number of things, in some embodiments said predetermined time period comprises 24 hours. People have routines that vary over a 24 hour period and thus, this is generally the most effective time period to analyse a user’s heart beat variations over.
  • the plurality of harmonics may comprise two or three harmonics in some embodiments said plurality of harmonics comprise four harmonics, said four harmonics comprising one day, a half day, a quarter of a day and an eighth of a day.
  • said sampling is performed over several days and said method further comprises the step of combining heart rate data for a same period of time from different days in said sampling period.
  • the data may be sensed over a single predetermined time period such as 24 hours, in some embodiments it is sensed over several days and the method comprises the step of combining heart rate data for a same period of time from different days in said sampling period.
  • the data from several time periods may be combined to improve the accuracy of the estimation.
  • said step of combining comprises weighting said data prior to said combining, higher heart rate data being given a lower weighting.
  • lower heart rate data is given a higher weighting than higher heart rate data.
  • Higher heart rate data may be indicative that the user is not currently resting but is involved in some activity and thus, the lower heart rate data is probably more typical of a resting heart rate.
  • the method further comprises determining at least one of sex and age of said user and adjusting said base pattern in dependence upon said at least one of said sex and age of said user prior to performing said fitting step.
  • the method further comprises determining said user’s activity levels and selecting heart rate data during periods of time where activity level is low and discarding heart rate data during periods of time where activity level is deemed to be high.
  • a user’ activity levels may be determined in a number of ways, in some cases there may be a sensor for sensing a user’s activity levels such as a step detector whose input is received alongside the heart rate data and can be used to discard data where the activity levels are high. In other cases, changes in heart rate maybe monitored and maybe used to determine where they rise that an activity has probably commenced and these higher levels can be discarded.
  • said method comprises applying a weighting to at least some of said user data prior to performing said combining step.
  • Weighting can be applied to the user data to assign more importance to some of said data than to others.
  • the model used to estimate resting heart rate is such that each data point used in the fitting step may be assigned a weight prior to the fitting step. This allows a more advanced analysis to be performed where the importance of certain data points can be uplifted or downgraded depending on circumstances. For example, a higher heart rate is indicative of a person moving and as such is less characteristic of the resting heart rate than other data. It may therefore be advantageous to apply a higher weight to lower heart rates than to higher heart rates. Furthermore, where for example, a real time streaming analysis is being performed then this may be achieved by appropriate weighting of data so that the method may apply a higher weight to newer more recently measured data than to older data. This allows the model to continually update the determination, and use of selected weighting values can be used to control this process.
  • said step of fitting comprises forcing said user’s data to have a same basic shape as said base pattern, said same basic shape having a freedom of a vertical translation, a scale factor and a horizontal translation with respect to said base pattern.
  • a computationally efficient way of fitting the data is by forcing the user’s data to have the same basic shape as the base pattern but providing it with the freedom of vertical translation, a scale factor and a horizontal translation with respect to the base pattern. Not only is this computationally efficient but it also provides an accurate indication of the user’s rest heart rate based on the assumption that users have similar periodic variations in their heart rate but that the resting heart rate may be a factor higher for some people, they may have larger differences between day and night resting rates and their sleep patterns may occur at different times of the day. These can be accounted for by the freedoms provided in fitting. In effect the refined user model is forced, after fitting the 3 parameters that are known to change, to have the same "shape" as the expected shape of circadian effect on heart rate.
  • said step of fitting comprises forcing said user’s data to have a same basic shape as said base pattern by performing harmonic regression on said data to force the shape of the variation in heart rate over time to be substantially the same as the base pattern, any variations between the base pattern and user’s pattern being in the scale factor of the shape the vertical translation of the shape , and in the horizontal translation or phase offset of the shape with respect to the base pattern.
  • harmonic regression can be performed on the data which will force the shape to have substantially the same shape as the base pattern.
  • said step of fitting comprises applying user data to the cosinor of the base pattern and determining a cost function by squaring the difference between measured heart rate and modelled heat rate weighted to favour lower heart rates, and determining an analytic solution that minimises the cost function.
  • said cost function to be minimised comprises a further regularisation term that adds a cost where the cosinor with the user’s data is far from the base pattern. Additionally further regularisation can be applied to the cost function this
  • the vertical translation of the basic shape to the base pattern provides an indication of amplitude difference in heart rate between night and day
  • the scale factor provides an indication of average resting heart rate
  • the horizontal translation provides an indication of sleep times of the user.
  • the amplitude difference is related to the difference in heart rate between night and day of a user compared to an average user, while the scale factor provides an indication of the average resting heart rate and the horizontal translation provides an indication of sleep times of the user and how they differ from the model which corresponds to the average user.
  • said step of determining said resting heart comprises determining at least one of an average resting heart rate and a resting heart rate as a function of time of day.
  • the resting heart rate can be determined as an average resting heart rate from the scale factor of the model for example, as explained above, the resting heart rate can also be determined as a function of time of day from the model itself. Both of these can be of interest to the user, the average resting heart rate providing an indication of fitness of a user for example, while the resting heart rate for the time of day being useful when trying to determine the activity of a user for example and how much their heart rate might have been increased by that activity.
  • the method comprises a further step of outputting an indication of said resting heart rate, wherein said indication comprises at least one of an average value of a determined resting heart rate, a current resting heart rate and an indication of fitness.
  • said at least some of said data comprises two surrogates derived from a measure indicative of a current resting heart rate and a time of the measure.
  • the method provides a computation that does not require a full data set but can perform the resting heart rate determination based on only two surrogates, these two surrogates being values derived from a measure of the resting heart rate and the time of the measure. This means the method does not require access to the full dataset, but only a limited set of values. All these values are moreover an additive function of data sets, which implies that they can be computed separately for each subset of samples, and then added together to obtain the total value. This allows the data to be accumulated directly in the user’s device, with big advantages in computational complexity, data transfer and privacy. The model is computationally cheap, depending linearly on the size of the data.
  • the method is such that the fitting of the data goes beyond the fitting of circadian activity to a resting heart rate and can be used not just to fit real, floating point data to a pattern, but to fit vectorial data such as complex data to different periodic patterns.
  • the vectorial data may include data from an accelerometer or gyroscope in addition to the heart rate data and can be processed by this method to fit data to non-periodic patterns using a linear combination of an arbitrary set of functions, for example, allowing a determination to be performed in multiple dimensions for multiple features.
  • said two surrogates comprise a shape coefficient S and Fourier convolution coefficient F.
  • the computation of the model does not need the full dataset, but in some
  • y is the j th measure of RHR of the user and Xj is the time of the measure and W j is the weight applied to the j th measure.
  • said at least some of said data is stored on said device.
  • the data accumulated on the device may be a corresponding subset allowing the other data to be discarded, this allows the model to be implemented in a streaming approach where the reduced data is accumulated on the device. This has important consequences for security and privacy of the data as it need never leave the device.
  • a second aspect provides a method of comparing a user’s heart rate to a predicted value, said method comprising: sensing a user’s activity level and determining an expected heart rate from an estimated increase in heart rate due to said sensed activity level and a determined resting heart rate for that time of day, said resting heart rate for said time of day being determined by a method according to a first aspect; outputting an indication of a difference in measured heart rate and predicted heart rate.
  • determining the resting heart rate for a period of time allows a user to determine from a current heart rate how much it has increased, the increase can then be used to determine how hard the user is working and perhaps as an indication of calories burnt.
  • the method comprises determining from said difference in measured heart rate and predicted heart rate a likelihood of said measured heart rate occurring.
  • the probability or likelihood of that heart rate for a user can be determined, the closer the value being to the predicted or expected value, the more likely it is to occur,
  • the method comprises determining a plurality of said likelihoods of a plurality of measured heart rates occurring, said plurality of measured heart rates being measured over a predetermined time period, and determining an average of said plurality of determined likelihoods during said time period.
  • said indication comprises an alert.
  • the average can calculated in a number of ways in some embodiments, the average comprises a geometric mean of said likelihood values for said time period.
  • said indication comprises a wellbeing indication.
  • the current resting heart rate may also be an indication of wellbeing an increased resting heart rate perhaps indicating either anxiety or an underlying illness.
  • a third aspect of the invention provides a method of determining a base pattern indicative of resting heart rate variations in an average person over a period of time, comprising: receiving data from a plurality of users indicating heart rate over said period of time; selecting heart rate data during periods of time where activity level is deemed to be low and discarding heart rate data during periods of time where activity level is deemed to be high; combining said data from multiple users and multiple days; generating a base pattern indicative of estimated changes in resting heart rate over time for an average person by fitting a periodic model to said combined data, said periodic model comprising a cosinor with a plurality of harmonics.
  • a base pattern is used against which the user’s heart variations over a time period are compared.
  • the base pattern should have shape that is indicative of a user’s heart rate variations over time.
  • One way of providing an effective and accurate base pattern is to generate it from data received from a plurality of users that is filtered by selecting a heart rate during periods of time when activity level is deemed to be low and combining this data for the multiple users and the multiple days and from this data generating the base pattern.
  • the base pattern is formed from a periodic model which comprises cosinor with a plurality of harmonics.
  • the inventors recognise that there is a periodic nature to heart rate variations and as such modelling it with a cosinor with a plurality of harmonics allows it be represented in a relatively accurate and yet computationally efficient manner.
  • said step of combining comprises an initial step of averaging heart rate data from each user for a same period of time in a day from a sample period of several days and coalescing said data for a plurality of users. Where the heart rate data being collected over several days then for each user a heart rate pattern for that user is determined by averaging the data for those days and then the data for the plurality of users is coalesced.
  • said step of coalescing comprises combining said data, said data being weighted prior to said combination, higher heart rate data having a lower weighting.
  • Activities and external factors can increase the heart rate of a user and thus, in order to improve accuracy and make the data more representative of the resting heart rate it may be advantageous to weight higher heart rate data so it has a decreased effect on the base pattern.
  • the weighting may be done at this point so that for the days where the heart rate data is higher at a particular period this heart rate data is weighted to provide less of a contribution to the final result than any lower heart rate data sampled for the same period.
  • the heart rate data with higher values may be given the lower weighting at the coalescing step where different users’ data is combined.
  • heart rate measures are influenced by factors such as mental stress, flu etc. and by providing this weighting more importance is given to points with a low heart rate, which are most likely to be unaffected by these external factors.
  • said step of fitting comprises using harmonic regression to said sampled data to fit said sampled data to said shape defined by said cosinor.
  • said plurality of harmonics comprise four harmonics, said four harmonics comprising one day, a half day, a quarter of a day and an eighth of a day.
  • a fourth aspect provides a method of determining a user’s resting heart rate according to a first aspect wherein said base pattern is determined according to a method according to a third aspect.
  • a fifth aspect provides a computer program comprising computer executable instructions which when executed by a processor are operable to control said processor to perform a method according to a first aspect, a second aspect or a third aspect.
  • a sixth aspect provides a device for determining a user’s resting heart rate, comprising: a sensor configured to continually sense said user’s heart rate over a period of time; processing circuitry configured to fit at least some of said sensed data to a base pattern indicative of estimated variations in an average person’s resting heart rate over a predetermined time period, said base pattern being modelled by a cosinor comprising a plurality of harmonics and to determine said resting heart rate from said sensed data fitted to said base pattern.
  • said processing circuitry is configured to estimate values for at least some of said intermittently received data during periods of time that said data is not received and to analyse and combine both said received data and estimated values.
  • Some of the data received from the sensors may be received continuously or almost continuously while other data is received intermittently.
  • the mathematical tools we developed adapt the received heart rate data of a user and in particular, that deemed to be resting heart rate data to the expected shape taking account of the circadian rhythm effect on resting heart rate.
  • the biometric data collected may be heart rate data and this may be fitted to a certain base pattern.
  • the data needed for this kind of analysis is sampled at a constant rate, i.e. evenly timed samples, e.g. every 5 minutes, or every 10 minutes.
  • our data contains missing datapoints and is unevenly sampled, so we developed the mathematical tools outlined in the description below to enable us to fit data that is not evenly sampled.
  • Figure l shows a flow diagram schematically illustrating a method of generating the base pattern
  • Figure 2 shows a flow diagram schematically showing a method of determining a user’s resting heart rate
  • Figures 3a to 3b shows the distribution of number of HR samples per user and of users per age
  • Figure 4 shows HR used for training the prior and the resulting prior for the circadian rhythm
  • Figure 8 Number of datapoint (logarithmic scale) by combination of minutes active in the last 5 minutes and in the last 20 minutes;
  • Figure 9 Residual mean by minutes active in the last 5 minutes and in the last 20 minutes;
  • Figure 10 Residual standard deviation by minutes active in the last 5 minutes and in the last 20 minutes;
  • Figure 14 HR of user 11 with circadian and activity prediction and probability of datapoint following the model
  • Figure 15 Circadian model for a user
  • Figure 16 Fitness as a function of q 0 ;
  • Figure 18 Distribution of fitness and risk for the users in the database.
  • a way of estimating resting heart rate is disclosed. This information may be used in the prediction of heart rate based on the moment of the day enabling one to determine if it is high or low.
  • a prior or base pattern for an average person is created from data measured from multiple users and a user’s heart rate is measured and fitted to this base pattern.
  • the base pattern is formed of a cosinor with multiple, preferably four harmonics and a user’s measured heart rate is forced to fit this shape.
  • the shape maybe horizontally translated to account for different sleep times of users such as night workers and students.
  • a vertical translation can be applied to account for differences in resting heart rate due to fitness levels for example, and a scale factor indicative of an amplitude difference in heart rates between night and day may also be applied.
  • any user’s determined shape should match that of the base pattern. It should be noted that the vertical translation representative of the resting heart rate and the amplitude being representative of the difference between night and day both correlate with the fitness level of the user, that is a lower heart rate and larger range usually means better health status.
  • expected HR in terms of circadian rhythm and physical activity is modelled.
  • latent variables are introduced that describe the general wellbeing of the user.
  • the first part of the model predicts the user resting heart rate as a function of time (circadian rhythm), accounting for differences between users.
  • the model will also take into account the change in heart rate caused by physical activity.
  • the complete model is able to predict the user’s heart rate for any time of the day and activity level. Using this model actual HR values can be analysed and the probability for each HR data point to the model, be sensor noise, be model noise (caused by factors not part of the model) can be estimated.
  • FIG. 1 shows a flow diagram illustrating steps in a method for generating the base pattern of an average user’s resting heart rate over a 24 hour period.
  • heart rate data is collected from multiple users over multiple days.
  • the data from each user is analysed in unit time periods and it is determined if during each time period the user is estimated to be active or not. This information may be derivable from a wearable device configured to monitor steps for example or it maybe derived from changes in the heart rate data itself. If it is determined that the user is not active during this time period, the data is included in the sampled data. If it is estimated that the user is active, the data is discarded.
  • the user’s data has been analysed for the whole 24 hour period, it is determined if the number of samples for the user is larger than a predetermined number and if it is the user’s data is added to the data for the generation of the prior. If it is not the user’s data is discarded. A subsequent user’s data is then analysed until all of the multiple users have been analysed. The collected data is then weighted so that lower heart rate data is given a higher weight than higher heart data as the lower heart rate data is more likely to be characteristic of a resting heart rate. The user’s data is then combined and fitted to a cosinor with multiple harmonics to generate a prior or base pattern.
  • This base pattern is then used in the analysis of individual’s data to estimate an individual’s resting heart rate as is shown schematically in figure 2 for example.
  • Figure 2 shows how the base pattern of Figure 1 might be used to estimate a user’s resting heart rate.
  • a user’s heart rate is monitored from a wearable device. The user will enter their age and sex and the base pattern generated by the method of Figure 1 will be adjusted to account for differences that it is assessed this will make to the average user’s heart rate pattern. The user’s heart rate is then fitted to the adjusted base pattern and a model of the user’s heart rate is generated. From this, an indication of the average resting heart rate for the user can be determined and output.
  • Subsequent steps may then be performed where the resting heart rate for the user at a particular time is derived from the model and compared with the measured heart rate of the user and the difference is output or used to estimate a current work rate of the user for example.
  • One example of further steps that may be performed comprises estimating a likelihood for each measure, that is if the measured heart rate is close to the expected heart rate then the likelihood of that measure is high, whereas if it is remote from this value the likelihood is low.
  • a set of likelihood values have been determined an average of these values during a time period is found, in some embodiments using the geometric mean.
  • This average value may then be compared with an expected value for a corresponding time window and where it is determined to be different to the expected value by more than a predetermined amount an alert may be triggered.
  • This alert may indicate abnormal physiological status, such as a stressful day, stressful meeting, flu, sleep disruptions or other things. In some cases an intervention may be triggered by the alert.
  • the time window maybe 30, 40, 50...
  • time windows of increasing size may be used. So that an initially small window with low computational overhead may be used and where this indicates a potential problem, this may trigger further analysis in a longer time window. It has been found that the time averaged likelihood of a measured value is a particularly accurate indicator of an abnormal physiological status. Further details of a specific example of the generation of a base pattern or prior for resting heart rate are provided below.
  • HR and HRV heart rate variable
  • Figures 3a and 3b provide a graphical representation of the different users in the sample group.
  • the accelerometer activity was analysed and activities were labelled as Walking, Automotive, Still, and other labels. This is to separate data collected while moving, where HR is unlikely to reflect the true resting HR, and data collected while the user was still, or typing, or commuting. Activities were separated in 2 classes: Active (that includes the Walking label ), Inactive (that includes all other labels).
  • a single cosinor is generally used to assess the effect of circadian rhythm on heart rate.
  • the shape of the HR as a function of the hour of the day significantly differs from a simple cosine: during the night the HR becomes slower for approximately 6 hours, and during the day it rises for approximately 18 hours, with 3 peaks
  • the a parameters are the amplitudes of the harmonics
  • the f parameters are the phases of the harmonics
  • t is the time, expressed in hours
  • Figure 4 shows the datapoints used for training and the resulting prior.
  • the shape of the prior captures the shape commonly found in literature for the effect of circadian rhythm on HR.
  • q 2 is the offset in phase with respect to the prior.
  • This model forces the shape of the circadian rhythm to be the same for all users, the same as the prior.
  • the only allowed changes are the average of the resting heart rate (0o), the amplitude of the oscillation between night and day (0i), and at what time the user goes to sleep and wakes up (the phase, 0 2 ).
  • Equation 5 We define a cost function J, shown in equation 5. Where f ⁇ is the model of equation 3 refined with user parameters, applied to all the measures (m), and y is the actual measured value. Y( ⁇ ) is the function of the prior for the circadian baseline.
  • the first term is similar to R 2 . However, because we expect external influences to make HR higher than expected (e.g. mental stress), we give more importance to y with low HR. This will make the model try to lower y instead of finding the average value.
  • the second term is a regularization term that adds a cost when f is far from the prior, behaving as a bayesian prior.
  • Figure 7 shows the distribution of Q by sex.
  • Figure 8 shows how many datapoints we have for each combination of activity values, in terms of number of minutes active in the last 5 minutes, and in the last 30 minutes. Because of the large disparity in number of datapoints, we show the log. We can see that for high values of activity in the last 20 minutes we have a small number of datapoints, statistics on that area should be handled with caution.
  • Figure 9 shows the average residuals (as relative error with respect to the actual HR) for each combination of activity levels.
  • the average residuals increase gradually from o to 0.13 as activity increases.
  • Table 1 shows the values.
  • Figure 10 shows the standard deviation of average residuals for each combination of activity levels. If we discard the outlier for o minutes in the last 5 minutes and 13 minutes in the last 20 minutes, the standard deviation gradually increases from 0.11 to 0.18 as activity levels increase. Table 2 shows the values.
  • Figure 11 shows the approximation of residuals using a linear model.
  • Figure 13 shows the distribution of the HR relative prediction error training a linear model, using activity as independent variables, for each user and predicting the HR (using a 50/50 split), against the Null Hypothesis that predicts the HR residual using the tables by minutes active previously shown (that are the same for all users).
  • Figure 14 shows 2 graphs.
  • the top graph shows the actual measured HR (black dots), circadian baseline (green line), predicted HR (red dots) with un-certainty (error bars).
  • the bottom graph shows, for every datapoint in the top graph, the probability that it is generated by the model.
  • RHR resting heart rate
  • RHR can be estimated from qq, that expresses the average RHR throughout the 24 hours.
  • the Maximum RHR is approximately equal to qq + 5Q1 and the minimum RHR is approximately qq Iqqi.
  • RHR oscillates between qo and 0o + 5 0i.
  • the fitness function F is defined as a sigmoid function with the flex at 70, as shown in equation 7 and Figure 16
  • the fitness function F is designed to report high values for 0 O below 50, normal values for 0 O between 50 and 90, and low values for 0 O above 90.
  • Figure 18 shows the distributions of the estimated user fitness, using the function F , and the estimated all-factors mortality risk, using the function R.
  • a further advantage of embodiments is that even with data that contains missing datapoints and is unevenly sampled, the mathematical tools are such as to enable the data that is not evenly sampled to be fitted to the model.
  • This is implemented at a mathematical level which is described in the following Periodic Pattern Fitting summary. It's an approach similar to a Fourier Transform (it works in the domain of frequency instead of time), but without the restrictions and assumptions of traditional Fourier analysis.
  • Periodic Pattern Fitting describes the problem that it solves starting from an abstract/high level approach, section 1, and considers special cases, every time more specialized, down to our special case (we want to fit our datapoints to a set of periodic functions, of known period, only allowing a limited set of parameters to change, thus preserving the "shape"). Section 2 explains how this is implemented numerically, and why it's computationally efficient.
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  • the model is computationally cheap, depending linearly on the size of the data.
  • the computation of the model does not need the full dataset, but only two surrogates ( F and S ), where the data is accumulated. This implies that the model can be implemented in a streaming approach, where the data is accumulated on the device, with important consequences for security and privacy of the data, which never leaves the user devices.
  • F and S surrogates
  • Physiological measures such as HR are continuous variables that are subject to the influence of external and internal stimulus changing over a daily cycle of about 24h with patterns that have been defined as circadian rhythms.
  • the time series obtained from wearable device are often noisy (i.e., variations in the biological system that are not part of the deterministic portion of the signal and that are derived from external errors such as instrument inaccuracy), short (i.e., low sampling) and sparse (i.e., unequal time intervals between observations).
  • noisy i.e., variations in the biological system that are not part of the deterministic portion of the signal and that are derived from external errors such as instrument inaccuracy
  • short i.e., low sampling
  • sparse i.e., unequal time intervals between observations.
  • the cosinor curve -with single component provides 3 parameters that describe the circadian rhythm: i) Mid-line Estimating Statistic Of Rhythm (MESOR) is an estimation of central tendency of the distribution of values across the cycles of the circadian rhythm computed using a cosine function; ii) Amplitude is the difference between the peak and the mean value of a wave; iii) Acrophase is the time of the day at which the peak of the circadian rhythm occurs.
  • MESOR Mid-line Estimating Statistic Of Rhythm
  • this is the first study that provides an algorithm able to predict the resting HR during (RHR) the day correcting the actual HR by the effect of external stimulus such as physical activity and stress status.
  • RHR resting HR during
  • the aim of this study is to define a non-sinusoidal model in order to assess the user’s resting HR on the base of the population resting HR circadian rhythms, while providing parameters that are easy to interpret.
  • the model proposed in our study provides the same three easy-to-interpret parameters which can be derived from the cosinor model with single component (i.e., MESOR, Amplitude, Acrophase ).
  • Our model allows the assignment of weights to every data point used for fitting the expected shape of to the user data. This allows the implementation of advanced analyses like assigning less importance to data points collected while the user was moving (expecting motion artefacts). Using weights also makes it possible to implement real-time streaming analysis of the data, performing a new analysis as new data arrives, assigning less importance to older data.
  • the model presented in this paper is computationally light and, for this reason, it is suitable to be executed on a wearable device.
  • the complexity of the accumulation phase is linear on the number of data points, while the complexity resolution phase depends on the number of frequencies used and not from the number of data points.
  • Equation 2 Equation 2
  • Equation 3 shows the formula that locks parameters of the c components only allowing 3 degrees of freedom (the same used in single component cosinor analysis). This is equivalent to single component cosinor analysis, using a different function than a cosine.
  • Equation 3 The free parameters in Equation 3 are:
  • Values of 0 ! close to 1 indicate that the range of the resting heart rate is similar to the prior, less than 1 indicate that the user resting heart rate has a smaller range, etc.;
  • q 2 the phase of the user circadian rhythm with respect to the phase of a cosine with period equal to one day. Values of q 2 close to o indicate that the user is sleeping at midday. q 2 ranges between -0.5 and 0.5.
  • the Q parameters allow to express the user RHR, U (h), as a vertical shift ( q 0 ), horizontal shift (q 2 ), and a change in amplitude (0 ! ) of the population prior A(h).
  • Equation 4 using the definition of U in Equation 3 into the following:
  • i(0) ⁇ w j yj + 0o ⁇ w ⁇ + Q 2 ⁇ 0 m 0 k ⁇ ; k+m S k+m
  • indices k and m range between— c and c.
  • the roots of the polynomial in can be found with spectral methods, i.e. using the eigenvalues of the companion matrix [9], and then refining the solutions from numerical error using the Newton- Raphson method.
  • Equation 9 depends on data indirectly through the values of F and S. Moreover, also the square loss function can be expressed in term of these values (and the total sum of yf). This means the whole algorithm does not require access to the full dataset, but only a limited set of values (namely the values of S, F and the sum of squares of y values if you want to output an absolute value for the loss).
  • the total complexity is thus 0(c 3 + Nc), in particular it only depends linearly on the size of data.
  • Figure 1 shows one of the priors fitted using the leave out-out approach.
  • the values for b and y, from equation 2 are:
  • ⁇ describes the first of the 4 components cosinor fitting.
  • the modulus expresses how important is this component in the fitting, and the argument expresses the phase of this component. has argument equal to zero, because we explicitly aligned all users to a cosine.
  • the first component captures 62% of the overall information, as the modulus of 1/q is equal to 0.62 multiplied by the sum of the moduli of all ⁇ , f 2 , f 3 , and f 4 .
  • Figure 2 shows the data of one day of a user, with the fitted single component cosinor model and our circadian model. We can see that our model better captures the sudden change in HR when the user awakens, and the fact that the time awake is longer than the time asleep.
  • Figure 3 shows seven days of HR and sleep data of one of the users, and the estimated circadian parameters:
  • the first graph shows the HR measures of the user as black dots, and the RHR as estimated by the circadian model as red dots;
  • the sleep data from the band it can be seen that on the fourth night the user suddenly changed sleep habits (from a healthy stable time to bed of about 11pm, to 3am).
  • the lack of proper sleep can be seen in the HR data and is reflected in the changes in 9 0 and q ⁇ .
  • the sudden change in the user sleep habit is reflected in the sudden change in q 2 ⁇
  • the cosinor RMSE is 5.73 ⁇ 2.33, our circadian model RMSE is 5.15 ⁇ 1.04.
  • Our circadian model RMSE is in average 10% lower than the cosinor RMSE.
  • a paired t-test returns, with a 95% confidence, a difference between cosinor RMSE and our circadian RMSE between 0.04 and 1.13 (p-value ⁇ 0.05).
  • the Null Hypothesis model has RMSE equal to 5.88 ⁇ I.86.
  • the loss function L ⁇ 9) can be used to calculate the standard error, useful to have an estimation of the distribution of the predicted data. This information could be used to automatically analyse HR activity, finding anomalous data points that could be caused by factors not modelled by circadian effect on RHR, such as physiological conditions.
  • the model is computationally cheap, depending linearly on the size of the data.
  • the computation of the model does not need the full dataset, but only two surrogates (F and S), where the data is accumulated. This implies that the model can be implemented in a streaming approach, where the data is accumulated on the device, with important consequences for security and privacy of the data, which never leaves the user devices.
  • the model is, to the best of our knowledge, the only computational model that can be used to predict users resting heart rate and to analyse the data using the parameters traditionally used to describe the circadian modulation of physiological activity.
  • the model we developed goes beyond fitting circadian activity on resting heart rate, and it can be used to fit arbitrary periodic real valued time series, but also vectorial data (e.g. gesture recognition from the accelerometer), or complex data. With an extension to the mathematical model it could be used to fit non periodic data using a linear combination of an arbitrary set of functions.
  • program storage devices e.g., digital data storage media, which are machine or computer readable and encode machine- executable or computer-executable programs of instructions, wherein said instructions perform some or all of the steps of said above-described methods.
  • the program storage devices maybe, e.g., digital memories, magnetic storage media such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media.
  • the embodiments are also intended to cover computers programmed to perform said steps of the above-described methods.

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Abstract

La présente invention concerne un procédé, un programme informatique et un dispositif de détermination d'une fréquence cardiaque au repos d'un•e utilisateur•trice. Le procédé comprend : la réception de données indicatrices d'une fréquence cardiaque d'un•e utilisateur•trice détectées sur une période de temps ; l'ajustement d'au moins une partie des données détectées à un profil de base indicatif des variations estimées dans une fréquence cardiaque moyenne au repos d'une personne sur une durée prédéterminée, le profil de base comprenant un cosinor comprenant une pluralité d'harmoniques ; et la détermination de la fréquence cardiaque au repos provenant des données détectées ajustées au profil de base.
PCT/GB2019/052849 2018-10-08 2019-10-08 Estimation de la fréquence cardiaque au repos WO2020074881A1 (fr)

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