Community Structure in Network Representation of Increments in Beat-to-beat Time Intervals of the Heart in Patients After Heart Transplantation

Abstract

Maxwell's demon is a special case of a feedback controlled system, where the information gathered by measurement is utilized by driving a system along a thermodynamic process that depends on the measurement outcome. The demon illustrates that with feedback one can design an engine that performs work by extracting energy from a single thermal bath. Besides the fundamental questions posed by the demon -the probabilistic nature of the Second Law, the relationship between entropy and information, etc.-there are other practical problems related to feedback engines. One of those is the design of optimal engines, protocols that extract the maximum amount of energy given some amount of information. A refinement of the second law to feedback systems establishes a bound to the extracted energy, a bound that is met by optimal feedback engines. It is also known that optimal engines are characterized by time reversibility. As a consequence, the optimal protocol given a measurement is the one that, run in reverse, prepares the system in the post-measurement state (preparation prescription). In this paper, we review these results and analyze some specific features of the preparation prescription when applied to non-ergodic systems.

Transition Network Entropy in Characterization of Complexity of Heart Rhythm After Heart Transplantation

“…The considerable success of the network approach motivated us to explore these ideas to identify patterns in RR-signals of people after HTX, and present them in a way which could be useful in clinical practice to observe the progress of reinnervation and the restoration of the function of autonomic regulation. This paper is a continuation of our earlier investigations (see [7][8][9][10]). Previously, we studied the emergence of complexity in transition networks constructed from RR-series [7,8], and from increments between subsequent RR-intervals [9,10].…”

“…This paper is a continuation of our earlier investigations (see [7][8][9][10]). Previously, we studied the emergence of complexity in transition networks constructed from RR-series [7,8], and from increments between subsequent RR-intervals [9,10]. In [9] we further studied networks representing fluctuations in the heart RR-intervals, and not the actual intervals.…”

“…Previously, we studied the emergence of complexity in transition networks constructed from RR-series [7,8], and from increments between subsequent RR-intervals [9,10]. In [9] we further studied networks representing fluctuations in the heart RR-intervals, and not the actual intervals. There, we investigated disintegration of such networks by measuring changes in the volume of the network remaining after subsequent removal of vertices which described events with a given increasing probability.…”

Dynamical Landscape of Heart Rhythm in Long-Term Heart Transplant Recipients: A Way to Discern Erratic Rhythms

“…Our concept of fragmentation includes zero value RR-increments. This extension is important because in the case of heart rhythms of HTX patients, we observe an abundance of zero RR-increments (Makowiec et al, 2013 , 2014 ).…”

Visualization of short-term heart period variability with network tools as a method for quantifying autonomic drive

“…By observing subsequent changes in RR-intervals, we obtain beat-to-beat information about the resulting force of these interactions. We have found that important dynamical aspects about the autonomic competitive regulation can be described by changes in RR-intervals, namely by RRincrements ( [20], [21]).…”