Change point detection by Filtered Derivative on the mean with p-Value method (FDpV) 

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HR analysis and change detection approach

Physical activities induce variation of the heart rate (HR), which is de ned as the number of heartbeats per minute (bpm). However, devices do not measure the heart rate, but instead the time interval between two successive R-waves. Indeed, the RR interval corresponds to the duration (in seconds) of each single cardiac cycle, see Fig.1.1. The two quantities are linked by the equation HR = 60=RR, and in this work, we will use indi erently both notations.
It is worth to note that the succession of RR intervals is called a tachogram. Except in the case of some very severe diseases, a heartbeat series uctuates. This phenomenon is known as heart rate variability (HRV). HRV has retained the attention of cardiologists, see [97] or [52] for a recent survey. Indeed, HRV re ects the regulation of HR and can contain invisible but relevant information. Therefore, heartbeat series are stochastic time dependent signals and almost as uctuating and complicated as nancial processes. One novelty of this work is the use of a theoretical probabilistic model combined with statistics for time series.
During the last two decades, many studies of HRV have been done. Some forget the dynamic structure of heartbeat series. Others analyze the dynamic structure of heartbeat series: A rst family of methods was introduced during the 1990’s and is based on spectral analysis. It consists in the computation of the spectral density in di erent bands of frequency  for instance High Frequency (HF) and Low Frequency (LF) ones by using the Fourier trans-form or the wavelet transform. The regulation of the HR is linked to the variation of the two quantities HF and LF , that is the variation in normalized units i.e. n.u (see [97] ). An apparently alternative set of methods is based on fractal analysis, see [59] or [52] and the references therein.
All methods assume, at least implicitly, that a heartbeat series is a stochastic process X depending on a d-dimensional parameter 2 IRd, where is a subset of the whole space. The parameter , which varies depending on the experimental conditions, is assumed to provide relevant informations on HR or HR regulation. Saying that the process X, also denoted by X , depends on parameter is equivalent to say that X belongs to a certain class of models M = fX ; 2 g. Next, the logical question becomes: Which stochastic model shall we use for heartbeat series? As pointed out by G. Box: « All models are wrong, but some are useful », and particularly simple models are easier and therefore more useful. In care centers, hospitals or laboratories, experimental conditions are under control and can be assumed to stay xed. As a corollary, the environment remains independent of time and a mathematical translation is provided by stationary process, namely a process whose structural parameters stay xed during time. In order to remain simple, we will also assume that the process is Gaussian.
The simplest stochastic model is provided by locally stationary Gaussian process, intro-duced by [38]. « Locally » means the existence of a segmentation = ( 1; : : : ; K ) such that the process X is a Gaussian stationary process on each sub-interval ( k; k+1) for k = 0; : : : ; K, where by convention 0 and K+1 are respectively the initial time and the nal time. Stress that K is the number of changes and can be equal to zero.
From a statistical point of view, this way of modelling addresses two sets of statistical questions: (1) Estimating the structural parameters of stationary Gaussian process, and (2) Fast change point analysis of these parameters knowing that recent technological progress allows recording and fast processing of large time series (40,000 or 100,000 or more).
Most of the methods suppose the stationarity of the signal, especially in time and fre-quency domains. The rst following subsection summarizes the static methods used to quantify HRV. The necessity of the dynamic approach in this framework is highlighted in the second subsection. Eventually, in the third subsection, we propose a new method of analysis for quantifying HRV.

Frequency domain analysis of HR series

The most widely used methods to assess HRV are frequency domain methods. Indeed, heartbeat signal is a time series, thus we can note another structural parameter which is time dependence or correlation structure. This correlation structure varies following the 3 di erent scales of time. This could be analyzed easily through Fourier Transform. Following recommendations of the Task Force (1996) (see [97]), we consider Fourier Transform of tachogram and the corresponding energy in Very Low Frequency, Low Frequency and High Frequency bands, denoted in the sequel by VLF, LF, HF. The VLF corresponds to frequencies under 0.03Hz, the LF corresponds to the frequency band [0.04Hz, 0.15Hz] and the HF deals with frequencies of the frequency band [0.15Hz,0.4Hz]. Actually, the state of the art in cardiology is to consider the energy of Fourier Transform into the three frequency bands VLF, LF, HF, and the ratio HF/LF. These di erent frequency bands are interpreted as referring to di erent regulation systems: the VLF have been attributed to the renin-angiotensin system (a hormone system that regulates blood pressure and uid balance), other humoral factors and thermoregulation, the LF is supposed to re ect the activity of the two components of the autonomous nervous system the orthosympathetic and parasympathetic while the HF band is the response of the parasympathetic activity majorly. In Fig.1.2, we can nd an illustration of these two systems.
Many studies have shown the inability of these methods known as traditional measures of HRV to detect subtle changes in RR series, see e.g. [84].
We prefer to base our statistical analysis on probabilistic modelling. The mathematical translation of a random signal with constant structural parameters is furnished by the notion of stationary process. This kind of process is well known in probability and widely used in engineering since the 1970’s. Its main feature is the existence of a spectral representation ([34]). However, in this study, we restrict ourselves to Gaussian process and recall that every zero mean stationary Gaussian process admits a harmonizable representation ([101]) Z X(t) = eit f1=2( )W (d ); for all t 2 IR; (1.1) IR.
where W (d ) is a complex Brownian measure chosen such that X is real valued, and f is an even function called the power spectral density. By adding the mean value , we shift to the case of stationary Gaussian process and expression (1.1) becomes: Z X(t) = + eit f1=2( )W (d ); for all t 2 IR.

Frequency and time domain analysis of HR series through change detection approach

The aim of this work is to detect change of the structural parameters of a heartbeat series that would mention a change in behaviour and so in biological functions. More precisely, we want to detect changes on the regulation of the heartbeats. The regulation is measured 6 through power spectral energy in the HF and LF bands. This real life analysis may be interesting in other cases such as athletes or in case of some pathologies needing continuous monitoring like neuropathogies. A rst step in this direction is reached in Subsection 1.4.3.1, where we build an index of physiological stress derived from change detection on the spectral power density in HF and LF frequency bands.
To this end, the theoretical framework used is that provided by the notion of locally stationary process ([38]). To avoid technicality, a signal X is locally stationary if there exists time segmentation = 1; : : : ; K+1, such that X is stationary on each interval ( k; k+1). K is the number of change points, and by convention the case K = 0 corresponds to stationary process with zero change points. For such locally Gaussian stationary process, we have the following spectral representation theorem Z X(t) = (t) + eit f1=2(t; ) dW ( ); for all t 2 R; (1.6) IR.

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Case of marathon runners

The studied cohort of marathoners is composed of ten non elite marathon runners. Before participation, all subjects were informed of the risks and the stress associated with the protocol, and gave their written voluntary informed consent. The protocol conformed to the standards set by the Declaration of Helsinki and its procedures were approved by the local ethics committee of the Saint Louis Hospital of Paris. Heart rate signal was recorded during Paris marathon in April 2006 using a cardio-frequency meter (Polar RS 800, FI). The race began at 8:45 am and a temperature of 17 C without wind ( < 2 m/s, anemometer, Windwatch, ALBA, Silva, Sweden) was observed. Two weeks prior to the race, the subjects performed a test to determine individual physical parameters ( V O2max and HRmax).

Case of shift workers

For eleven shift workers, measures are made using Spiderview of ELA Medical (Sorin Group Company), a very compact numeric Holter recorder. It runs on batteries and can make recordings of 24 hours continuously at the workplace. It is worn on a belt or a shoulder, and is not cumbersome. Its 5 adhesive electrodes receive the signal by two derivations and insure reliable recording. Controlling the quality of the recording is possible from the installation of the electrodes and the viewing patterns on screen graphics [?]. The data are stored on a memory card. High-resolution ECGs (1000Hz, 2.5 V) are obtained.

Pre-processing HR data

Heart rate recording during exercise is not an easy work because it is realized in \free-running » conditions and not within controlled clinical conditions. Indeed, bad contact be-tween the worker’s skin and the frequency meter added to the possible bad manipulation of the device may induce the presence of aberrant data.
It is worth noting that the size of our data series ranges from 30,000 (for marathon runners) to 150,000 (for shift workers), so it would take much time to carry on all the changes and corrections in order to get an exploitable series of data for further study. While focusing on the previous works, we found that most of them make a part of the corrections of what they call « ectopic beats » ([36]), « premature beats » or noise ([85]) manually with the help of an « experienced observer » ([93]). So, the use of these techniques is di erent from a work to another and is not practical for huge data sets. That being said, it exists programs used to analyze such recordings in hospitals which are implemented for sick people; consequently interpretations can be inappropriate or wrong in case of healthy subjects. For example, for a high level athlete, the interval between two heartbeats can easily reach 450 ms (133 bpm) which is abnormal in the case of people lying in hospital.
For that purpose, and by referring to physiological arguments, we developed a technique named \Tachogram cleaning »1 capable to automatically identify artifacts and correct them in healthy subjects’heartbeat series. « Tachogram Cleaning » corrects aberrant data by referring to physiological arguments rather than statistical ones.
Let us take a look on a tachogram (recorded following speci cations of Paragraph 1.3.2.1) of a runner in Fig.5.1 before processing artefatcs. We can denote in Fig.5.1 some « unexpected » data values that we designate by « artefcts » and for which it is di cult to determine the cause. The result of pre-processing data series of B1 is shown in Fig.5.7 in yellow line.

Table of contents :

Introduction
1 Heart rate analysis through mean change point detection: Case study of marathoners 
1.1 Introduction
1.2 HR analysis and change detection approach
1.2.1 Frequency domain analysis of HR series
1.2.2 Frequency and time domain analysis of HR series through change detection approach
1.2.2.1 Change detection on the mean
1.2.2.2 Change detection on the spectral density
1.3 Experiment and data
1.3.1 Subjects
1.3.2 Data acquisition and pre-processing
1.3.2.1 Case of marathon runners
1.3.2.2 Case of shift workers
1.3.3 Pre-processing HR data
1.4 Results
1.4.1 Results for marathon runners
1.4.2 Results for shift workers
1.4.3 The two cohorts study
1.4.3.1 Statistical study of the cohorts
1.4.3.2 Results
1.5 Discussion
1.6 Conclusion
2 Change point detection by Filtered Derivative on the mean with p-Value method (FDpV) 
2.1 Introduction
2.2 FDpV for change detection: a two step procedure
2.3 Some FDpV’s applications: examples of academic and real cases
2.3.1 Case of change detection on the mean
2.3.2 Case of change detection on the EDA signal
2.4 Discussion
2.5 Conclusion
3 Experimental protocol dedicated for marathoners state change assessment based on Electrodermal activity (EDA) measurement 
3.1 In vivo pre-test experimentation with embedded sensors: Competition of Foulees du Lac
3.1.1 Population
3.1.2 Sensors for HR, EDA and respiration measurement
3.1.3 Faced issues
3.1.4 Towards a dedicated protocol for EDA measurement
3.2 EDA for state change detection
3.2.1 EDA versus HR
3.2.2 EDA indicators of state changes
3.2.3 EDA measurement
3.2.4 The Q sensor
3.3 Some possible EDA features and artefacts measurement
3.3.1 Motion artefact
3.3.2 Artefact due to mis-use of the sensor
3.3.2.1 Artefacts related to moved or detached electrodes
3.3.2.2 Missed data and zero values
3.3.3 Particular EDA feature: the storm
3.4 Comar Marathon with a well established protocol
3.4.1 Principle of the Comar experiment
3.4.2 Execution of the experience
3.4.3 Presentation of the protocol
3.4.4 Evaluation of the Comar protocol: data validation
3.5 Conclusion
4 Temporal signatures of electrodermal activity (EDA) for the evaluation of runners’performance: start and nish phases 
4.1 Introduction
4.2 Protocol and data collection
4.2.1 Frame of the experiment
4.2.2 Population and classes of participants
4.2.3 Materials
4.3 Pre-processing
4.3.1 EDA artefacts identication
4.3.2 EDA special feature: The storm
4.4 Preliminary EDA analysis on a reference runner (P6)
4.5 Athletes EDA signature: the start and the nish phases
4.5.1 Temporal signature and EDA level of the start phase of the competition
4.5.1.1 Temporal signature of the start phase
4.5.1.2 EDA level at the start phase
4.5.2 Temporal signature and EDA level at the nish phase of a competition
4.5.2.1 Temporal signature of the nish phase
4.5.2.2 EDA level at the nish phase
4.6 Electrodermal reactions at the start and the nish phases
4.7 Conclusion
4.8 References
5 Tonic level and phasic activity extraction and motion artefact and special events detection 
5.1 Introduction
5.2 EMD for EDA tonic level extraction
5.2.1 EDA tonic level extraction
5.2.2 EMD approach
5.2.3 IMF aggregation strategy for estimating EDA tonic component[73, 74]
5.3 EDA signal analysis: Case study of a marathon runner
5.3.1 EDA tonic level: extraction via EMD components aggregation
5.3.2 Pseudo periodic artefact detection via EMD components
5.4 Change point detection on IMF components of the EDA signal
5.5 Conclusion
Appendices 
A Conception of an experimental protocol 
B Participant form 
C Sensor form 
Bibliography

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