Modeling the Temporal Sequence Parametersin surrogate data of cardiovascular oscillations

Abstract

<p>The short-term cardiovascular oscillations are primarily governed by the baroreceptor<br />reflex (BRR) feedback loop and respiration. Their analysis presents important issue<br />for assessment of cardiovascular health, as baroreflex impairment is associated with<br />major cardiovascular disease. Technological advances made noninvasive real-time<br />measurements of cardiovascular variabilities (CVV) possible and inexpensive. The<br />commercial devices for electrocardiogram (ECG) and blood pressure (BP) acquisition<br />usually have integrated modules for consequent signal analysis, thus providing the<br />basic indexes related to CVVs.<br />Besides the physiological role of BRR in cardiovascular homeostasis,there is a<br />growing evidence that changes in baroreflex function reflect the changes in cardio-<br />vascular regulation and underlying regulatory mechanisms governed by autonomic<br />nervous system (ANS). Therefore, measuring baroreflex function provides insight<br />into ANS functioning, which is otherwise unavailable in nonivasive manner. Actu-<br />ally, the major breakthrough in the investigation of CVVs is primarily driven by this<br />fact.<br />Despite the abundance of methods reported in the literature, there is still no<br />gold standard for assessment of dynamic baroreflex gain (BRS - baroreflex sensitiv-<br />ity). The most widely used method for BRS assessment integrated in most of the<br />commercial platforms is the sequence technique, which offers BRS estimate implying<br />linear relationship between systolic (S)BP and the RR intervals, the intervals between<br />two consecutive heart beats. There is a number of implementations of this method,<br />adjusted to specific species requirements, thus further broadening methodological<br />diversity.<br />The sequence method is based on the computerized scanning of beat-to-beat series<br />of SBP and RR interval values in search of spontaneous SBP monotonic pressure<br />changes (SBP ramps) over at least three or more consecutive heart beats followed<br />iiiby unidirectional RR monotonic changes (RR ramp) thus forming the barorelfex<br />sequence. Monotonic pressure changes are thus buffered via BRR feedback loop<br />resulting in the adequate reaction on heart rate to oppose the unwanted monotonic<br />SBP change.<br />Besides the BRS estimate, the sequence method yields a number of parameters<br />characterizing SBP and RR series and effectiveness of baroreflex. In this thesis the<br />sequence coverage area (SCA)[ms&middot;mmHg] is introduced as the new parameter which<br />enables quantitative assessment of the BRR operating range. SCAadditionally im-<br />proved the visual representation of the re-setting phenomena. Further refinement<br />of SCA with more precise contour plots offers improvement in the operating area<br />assessment at the same time reflecting the density of the sequence points. The thor-<br />ough analysis of the BRS changes during and after exposure to acute and chronic<br />stress is provided with novel parameters incorporated into analysis to contribute to<br />the elucidating the effects of stress on cardiovascular regulation.<br />Most of commercially available medical devices for monitoring cardiovascular<br />function use the sequence technique mainly for its simplicity: ease of implemen-<br />tation and interpretation. Yet, the series of requiring engineering tasks precedes the<br />proper implementation of this seemingly easy procedure. The precondition for valid<br />BRS assessment is the correct delineation of the ECG and BP waveforms to extract<br />the SBP and RR interval series. The problems encountered mainly stem from the<br />measurement artifacts, inter-subject waveform variabilities andcharacteristic changes<br />caused by pathology which are very often indistinguishable from noise. The lack of<br />delineation performance has to be compensated by the preprocessing of the SBP and<br />RR interval series to ensure their consistent phase relationship. In this thesis the se-<br />ries of encountered problems and solutions are presented, to draw attention to these<br />important methodological issues.<br />Another important issue regarding sequence technique is the non-selective in-<br />clusion of all the sequences meeting the imposed criteria in BRS estimation. The<br />question is whether these sequences reflect true physiological RRand SBP (barore-<br />flex or non barorefex) interactions or accidental, random occurrences. To overcome<br />this problem more rigid criteria for sequence validation can be imposed, but this will<br />further deepen the problem of absence of baroreflex sequences in cases of autonomic<br />dysfunction, which would render the sequence method unusable.<br />To test the hypothesis whether the found baroreflex sequencespresent physio-<br />logical responses the method of surrogate data is used. The method of surrogate<br />data stems from the family of powerful resampling procedures andso far has been<br />successfully used to explore the underlying patterns within data. Different types of<br />surrogate data can be used to investigate the type of SBP-RR interactions, but the<br />thesis focuses on isodistributional (ID) surrogate data which arethe random shuffleof the original series preserving the mean, variance and histogramof original data,<br />thus representing the constrained realizations.<br />The number of baroreflex sequences in original and ID surrogate data are com-<br />pared to rule out the possibility of their random origination. For these purposes for<br />each original series SBP-RR pair a number of surrogate data pairs has to be gener-<br />ated. The number of produced surrogates determines the powerof the test, thus it<br />is dependent on the set significance level. The time averages of BRR parameters are<br />calculated for the ensemble of surrogate realizations to be compared to the values<br />calculated from original series.<br />Even though the increased computational power fosters the bootstrap like proce-<br />dures, in some cases it is possible to yield analytic solution which renderthe surrogate<br />generation and analysis excessive. Having in mind the frequent usage of the sequence<br />technique and the following exhausting surrogate testing, the main contribution of<br />this thesis is the model developed to derive the formulae for the temporal sequence<br />parameters (distribution, length, and number of sequences) in IDsurrogate data.<br />The obtained expressions present the ensemble averages of these sequence method<br />parameters i.e. their expected numbers as functions of the minimalsequence length,<br />the amplitude threshold and the length Nof the observed SBP-RR time series. The<br />model is in a form of a discrete, homogeneous, and ergodic Markov chain describing<br />successive increases and decreases of SBP-RR amplitudes in ID surrogate data.<br />The derived formulae eliminated the need for surrogate data generation and anal-<br />ysis, presenting fast and easy plug-in tool for measuring the degree of randomness in<br />sequences estimated from the original SBP-RR time series.</p>