Time-frequency analysis for the dynamic quantification of the interactions between signals related to the cardiovascular system

In this dissertation, some advanced methodologies for the study of non-stationary signals in the joint time-frequency (TF) domain are presented, with the purpose of characterizing the dynamic interactions between cardiovascular signals. This study is motivated by the necessity of improving the understanding of the Autonomic control of the cardiovascular system, whose impairment is related with many pathologies. The dissertation is articulated in three parts: An introduction in which relevant physiological and methodological aspects are described; a methodological part in which TF synthesis as well as TF spectral, coherence and phase difference analysis are described; and a part in which the proposed methodologies are applied to physiological studies. In the introduction, the control of sympathetic and parasympathetic nervous systems on the cardiovascular regulation as well as the interactions between cardiovascular parameters and respiration are described. In particular, the physiological mechanisms that are still unclear or that are currently matter of debate are highlighted. To better contextualize the work proposed in the dissertation, a description of the most recent time-varying techniques of analysis is also given. The second part is composed of four chapters, §2-§5, which face the following issues: simulation of non-stationary signals, spectral analysis, coherence analysis and phase analysis in the TF domain. In chapter §2, a method to generate non-stationary stochastic processes which mimic the dynamics of cardiovascular signals is described. These processes are characterized by a predetermined and controlled TF structure: the design parameters that are used as input of the model are either the instantaneous frequency and power or the instantaneous frequency and spectral amplitude of each spectral component, and the output is the stochastic process associated to them. The accuracy and robustness of the method are evaluated in simulation studies which aim at simulating heart rate variability during exercise stress test and listening to different music excerpts. In chapter §3, the TF distributions belonging to the Cohen's class are introduced. In particular, the smoothed pseudo Wigner-Ville distribution (SPWVD) is described. Owing to the possibility of performing an independent smoothing in time and frequency, the SPWVD is considered one of the best options to analyze non-stationary signals. A method to quantify the TF resolution of these distributions is proposed and it is used throughout the entire dissertation. A simulation study based on signals generated by means of the method presented in chapter §2 is carried out to evaluate the accuracy of the SPWVD in conditions characterized by different degree of non-stationarity. Finally, a method that performs a parametric decomposition of the SPWVD is described. The advantage of this method, which will be used in a physiological study in chapter §6, is that it allows separating relevant signal components from noise, thus offering the possibility of reducing the interference terms that usually appear in the distributions of the Cohen's class. Chapter §4 is about the estimation of time-frequency coherence between non-stationary signals. Time-frequency coherence has the advantage of allowing the simultaneous localization of temporal intervals and spectral bands in which two signals are locally correlated, thus providing robust and accurate tracking of local correlation changes. Coherence estimates depend on the TF resolution of the distribution used in the estimation. To give a correct interpretation of the results, two methods based on surrogate data are proposed to assess whether the coherence estimates are statistically significant. Two algorithms to automatically determine signal-dependent kernels which allow estimating TF coherence by SPWVD are proposed. In a comparative study which involve both simulated and physiological recorded data, the SPWVD is shown to localize with higher accuracy than other distributions, such as the multitaper spectrogram (MTSP) and the continuous wavelet transform, the TF regions in which signals are locally correlated. Finally, an example of application of TF coherence analysis on cardiovascular signals, such as heart period variability, systolic arterial pressure variability and respiration, is given. Chapter §5 is about the estimation of phase differences between cardiovascular signals in the TF domain. Time-frequency phase difference analysis allows a fast tracking of the variation of the degree of synchronization between the spectral components of two signals. Moreover, phase difference information can be used to establish, to a certain degree, causal relationships between non-stationary spectral components. The use of the SPWVD to estimate TF phase differences is particularly suited because TF phase difference estimates are reliable only around well localized time-varying spectral band in which spectral components are locally correlated. The proposed methodology is evaluated in different simulation studies based on both computer generated and recorded physiological data. In the second part of the dissertation, composed of chapters §6-§8, three physiological studies are described. In chapter §6, the effect that musical excerpts characterized by different emotional valence has on HRV and respiration is studied. The characterization of the influence of music on cardiovascular parameters has both physiological and clinical relevance, since the use of music for therapeutic purposes is a matter of increasing interest. In this study, it is shown that the emotional valence of music specifically affects the respiratory frequency and the respiratory oscillations in HRV. It is shown that the transition from a musical stimulus to another provokes variations characterized by a first rapid response, which lasts about 10-20 seconds, and a seconds slower phase, which last more than one minute. The cardio-respiratory interactions are also studied. It is shown that musical excerpts characterized by different emotional valence do not provoke different pattern of response in the coherence and phase differences between HRV and respiration. In chapter §7 the degree of similarity between the TF structure of HRV and the pulse rate variability (PRV) obtained from the photoplethysmography (PPG) signal, during tilt table test, is studied. The aim of the study is to assess whether PRV can be used as a surrogate for HRV during non-stationary conditions. The use of PRV to indirectly estimate HRV is interesting since the device used to estimate the PPG signal is not cumbersome, is cheap, and widely used in the clinical environment. Time-frequency and TF coherence analysis suggest that PRV can be used as alternative measurement of the HRV, at least during tilt table test. The study also reveals that some differences between HRV and PRV also exist, especially in the oscillations related with respiration. However, in the analyzed signals, these differences, which are due to variations in the pulse transit time, are not sufficient to modify the conclusions of the physiological study. In chapter §8, the cross TF analysis presented in chapters §4-§5 is applied to the study of the dynamic interactions between RRV and systolic arterial pressure variability (SAPV). The study of these interactions is interesting because they are still partially unclear, and because of the clinical relevance of baroreflex sensitivity, which has both diagnostic and prognostic value. This study shows that during tilt table test, postural changes provoke a fast decrease in the baroreflex sensitivity and phase changes between RRV and SAPV. In another data base, the indices obtained by TF analysis allows discriminating between healthy subjects and subjects with autonomic dysfunctions.