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Error analysis (Mathematics) --- Least squares --- Congresses

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Operational research. Game theory --- Moindres carrés --- Least squares --- Academic collection --- #TELE:SISTA --- 519.6 --- Method of least squares --- Squares, Least --- Curve fitting --- Geodesy --- Mathematical statistics --- Mathematics --- Probabilities --- Triangulation --- Computational mathematics. Numerical analysis. Computer programming --- Least squares. --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Moindres carrés

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Least squares

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The rate at which our heart beats, is a dynamical process enabling adaptive changes according to the demands of our body. These variations in heart rate are widely studied in so-called heart rate variability (HRV) analyses, as they contain much information about the activity of our autonomic nervous system. Variability in the heart rate arises from several processes, such as thermoregulation, hormones, arterial blood pressure, respiration, etc. One of the main short-term modulators of the heart rate is respiration. This phenomenon is called respiratory sinus arrhythmia (RSA) and comprises the rhythmic fluctuation of the heart rate at respiratory frequency. It has also widely been used as an index of vagal outflow. However, this has been widely debated as some studies have shown that the magnitude of RSA changes with respiratory rate and the depth of breathing, independently of parasympathetic activity. It is therefore questioned whether RSA represents a true index of vagal outflow. The lack of consensus on the precise mechanisms that are responsible for this cardiorespiratory interaction, lead to interpretational problems. It is nevertheless apparent that it is important to include information of respiration when interpretations of HRV studies are conducted. Inspired by the polemic nature of this debate on the interpretation of RSA, this dissertation focuses on three topics. The first part of the thesis deals with the development of a surrogate respiratory signal based on ECG recordings. This is termed ECG-derived respiration (EDR). It is an important topic to cope retrospectively with possible confounding respiratory parameters in HRV studies without separate respiratory recordings. Additionally, with the trend towards less obtrusive and more cost-efficient monitoring, the possibility to obtain reliable EDR signals would discard the need to separately record respiration using specialized equipment, that often also interferes with natural breathing. In this dissertation, a new algorithm is proposed for single lead ECGs and compared with state-of-the-art EDR methods. The second focus of the thesis is closely related to the interpretational problems concerning RSA and cardiac vagal activity. As such, the aim is to separate the tachogram in two components: one that is strictly related to respiration, and another component that is unrelated to respiration. Several methods to realize this separation have been proposed in the literature, and an extensive comparison is conducted in this thesis. Additionally, a separation method based on partial time-frequency analyses is discussed. It has the advantage over other methods that it can deal with nonstationary signals. The last part of this dissertation focuses on the characterization of common dynamics in HRV and respiration. It is well-known that the interactions that play in the cardiorespiratory system are complex. Although the common dynamics have been studied in the literature using techniques like synchronization, symbolic dynamics and coupled oscillators, the precise mechanisms are still unclear. Therefore, we aim to characterize the common dynamics in a different way in order to gain more insight in the underlying cardiorespiratory mechanisms and their interpretation. In particular, information-theoretic measures that quantify the information storage and internal information of HRV, and the information transfer and cross information from respiration to HRV are discussed. Throughout this dissertation, special attention is also paid to the application of mental stress monitoring. It has been found that persons who are chronically stressed, have an increased risk for cardiovascular diseases. Also breathing plays an important role, as research suggests that respiration can be used as an interface to deal with negative effects of mental stress, and thus alter cardiac autonomic activity. This makes mental stress an interesting application on which the impact of the last two topics is evaluated.

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