Purpose: We investigated motor-respiratory coordination (MRC) in visually guided forearm tracking movements focusing on two main questions: (1) Does attentional demand, training or complexity of the tracking task have an effect on the degree of MRC? (2) Does MRC impair the precision of those movements? We hypothesized that (1) enhanced attention to the tracking task and training increase the degree of MRC while higher task complexity would reduce it, and (2) MRC impairs tracking precision. Methods: Thirty-five volunteers performed eight tracking trials with several conditions: positive (direct) signal–response relation (SRR), negative (inverse) SRR to increase task complexity, specific instruction for enhanced attention to maximize tracking precision (“strict” instruction), and specific instruction that tracking precision would not be evaluated (“relaxed” instruction). The trials with positive and negative SRR were performed three times each to study training effects. Results: While the degree of MRC remained in the same range throughout all experimental conditions, a switch in phase-coupling pattern was observed. In conditions with positive SRR or with relaxed instruction, we found one preferred phase-relationship per period. With higher task complexity (negative SRR) or increased attentional demand (strict instruction), a tighter coupling pattern with two preferred phase-relationships per period was adopted. Our main result was that MRC improved tracking precision in all conditions except for that with relaxed instruction. Reduction of amplitude errors mainly contributed to this precision improvement. Conclusion: These results suggest that attention devoted to a precision movement intensifies its phase-coupling with breathing and enhances MRC-related improvement of tracking precision.

In der vorliegenden Dissertation wird eine Beschreibung der Phasendynamik irregulärer Oszillationen und deren Wechselwirkungen vorgestellt. Hierbei werden chaotische und stochastische Oszillationen autonomer dissipativer Systeme betrachtet. Für eine Phasenbeschreibung stochastischer Oszillationen müssen zum einen unterschiedliche Werte der Phase zueinander in Beziehung gesetzt werden, um ihre Dynamik unabhängig von der gewählten Parametrisierung der Oszillation beschreiben zu können. Zum anderen müssen für stochastische und chaotische Oszillationen diejenigen Systemzustände identifiziert werden, die sich in der gleichen Phase befinden. Im Rahmen dieser Dissertation werden die Werte der Phase über eine gemittelte Phasengeschwindigkeitsfunktion miteinander in Beziehung gesetzt. Für stochastische Oszillationen sind jedoch verschiedene Definitionen der mittleren Geschwindigkeit möglich. Um die Unterschiede der Geschwindigkeitsdefinitionen besser zu verstehen, werden auf ihrer Basis effektive deterministische Modelle der Oszillationen konstruiert. Hierbei zeigt sich, dass die Modelle unterschiedliche Oszillationseigenschaften, wie z. B. die mittlere Frequenz oder die invariante Wahrscheinlichkeitsverteilung, nachahmen. Je nach Anwendung stellt die effektive Phasengeschwindigkeitsfunktion eines speziellen Modells eine zweckmäßige Phasenbeziehung her. Wie anhand einfacher Beispiele erklärt wird, kann so die Theorie der effektiven Phasendynamik auch kontinuierlich und pulsartig wechselwirkende stochastische Oszillationen beschreiben. Weiterhin wird ein Kriterium für die invariante Identifikation von Zuständen gleicher Phase irregulärer Oszillationen zu sogenannten generalisierten Isophasen beschrieben: Die Zustände einer solchen Isophase sollen in ihrer dynamischen Entwicklung ununterscheidbar werden. Für stochastische Oszillationen wird dieses Kriterium in einem mittleren Sinne interpretiert. Wie anhand von Beispielen demonstriert wird, lassen sich so verschiedene Typen stochastischer Oszillationen in einheitlicher Weise auf eine stochastische Phasendynamik reduzieren. Mit Hilfe eines numerischen Algorithmus zur Schätzung der Isophasen aus Daten wird die Anwendbarkeit der Theorie anhand eines Signals regelmäßiger Atmung gezeigt. Weiterhin zeigt sich, dass das Kriterium der Phasenidentifikation für chaotische Oszillationen nur approximativ erfüllt werden kann. Anhand des Rössleroszillators wird der tiefgreifende Zusammenhang zwischen approximativen Isophasen, chaotischer Phasendiffusion und instabilen periodischen Orbits dargelegt. Gemeinsam ermöglichen die Theorien der effektiven Phasendynamik und der generalisierten Isophasen eine umfassende und einheitliche Phasenbeschreibung irregulärer Oszillationen. / Many natural systems embedded in a complex surrounding show irregular oscillatory dynamics. The oscillations can be parameterized by a phase variable in order to obtain a simplified theoretical description of the dynamics. Importantly, a phase description can be easily extended to describe the interactions of the system with its surrounding. It is desirable to define an invariant phase that is independent of the observable or the arbitrary parameterization, in order to make, for example, the phase characteristics obtained from different experiments comparable. In this thesis, we present an invariant phase description of irregular oscillations and their interactions with the surrounding. The description is applicable to stochastic and chaotic irregular oscillations of autonomous dissipative systems. For this it is necessary to interrelate different phase values in order to allow for a parameterization-independent phase definition. On the other hand, a criterion is needed, that invariantly identifies the system states that are in the same phase. To allow for a parameterization-independent definition of phase, we interrelate different phase values by the phase velocity. However, the treatment of stochastic oscillations is complicated by the fact that different definitions of average velocity are possible. For a better understanding of their differences, we analyse effective deterministic phase models of the oscillations based upon the different velocity definitions. Dependent on the application, a certain effective velocity is suitable for a parameterization-independent phase description. In this way, continuous as well pulse-like interactions of stochastic oscillations can be described, as it is demonstrated with simple examples. On the other hand, an invariant criterion of identification is proposed that generalizes the concept of standard (Winfree) isophases. System states of the same phase are identified to belong to the same generalized isophase using the following invariant criterion: All states of an isophase shall become indistinguishable in the course of time. The criterion is interpreted in an average sense for stochastic oscillations. It allows for a unified treatment of different types of stochastic oscillations. Using a numerical estimation algorithm of isophases, the applicability of the theory is demonstrated by a signal of regular human respiration. For chaotic oscillations, generalized isophases can only be obtained up to a certain approximation. The intimate relationship between these approximate isophase, chaotic phase diffusion, and unstable periodic orbits is explained with the example of the chaotic roes oscillator. Together, the concept of generalized isophases and the effective phase theory allow for a unified, and invariant phase description of stochastic and chaotic irregular oscillations.

Purpose: We investigated motor-respiratory coordination (MRC) in visually guided forearm tracking movements focusing on two main questions: (1) Does attentional demand, training or complexity of the tracking task have an effect on the degree of MRC? (2) Does MRC impair the precision of those movements? We hypothesized that (1) enhanced attention to the tracking task and training increase the degree of MRC while higher task complexity would reduce it, and (2) MRC impairs tracking precision. Methods: Thirty-five volunteers performed eight tracking trials with several conditions: positive (direct) signal–response relation (SRR), negative (inverse) SRR to increase task complexity, specific instruction for enhanced attention to maximize tracking precision (“strict” instruction), and specific instruction that tracking precision would not be evaluated (“relaxed” instruction). The trials with positive and negative SRR were performed three times each to study training effects. Results: While the degree of MRC remained in the same range throughout all experimental conditions, a switch in phase-coupling pattern was observed. In conditions with positive SRR or with relaxed instruction, we found one preferred phase-relationship per period. With higher task complexity (negative SRR) or increased attentional demand (strict instruction), a tighter coupling pattern with two preferred phase-relationships per period was adopted. Our main result was that MRC improved tracking precision in all conditions except for that with relaxed instruction. Reduction of amplitude errors mainly contributed to this precision improvement. Conclusion: These results suggest that attention devoted to a precision movement intensifies its phase-coupling with breathing and enhances MRC-related improvement of tracking precision.