Complexity and emergent phenomena

Complex biological systems operate under non-equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power-law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory-related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed.

Study of time reversibility/irreversibility of cardiovascular data: theoretical results and application to laser Doppler flowmetry and heart rate variability signals

Time irreversibility can be qualitatively defined as the degree of a signal for temporal asymmetry. Recently, a time irreversibility characterization method based on entropies of positive and negative increments has been proposed for experimental signals and applied to heart rate variability (HRV) data (central cardiovascular system (CVS)). The results led to interesting information as a time asymmetry index was found different for young subjects and elderly people or heart disease patients. Nevertheless, similar analyses have not yet been conducted on laser Doppler flowmetry (LDF) signals (peripheral CVS). We first propose to further investigate the above-mentioned characterization method. Then, LDF signals, LDF signals reduced to samples acquired during ECG R peaks (LDF_R(ECG) signals) and HRV recorded simultaneously in healthy subjects are processed. Entropies of positive and negative increments for LDF signals show a nonmonotonic pattern: oscillations--more or less pronounced, depending on subjects--are found with a period matching the one of cardiac activity. However, such oscillations are not found with LDF_R(ECG) nor with HRV. Moreover, the asymmetry index for LDF is markedly different from the ones of LDF_R(ECG) and HRV. The cardiac activity may therefore play a dominant role in the time irreversibility properties of LDF signals.

Multiscale entropy of laser Doppler flowmetry signals in healthy human subjects

PURPOSE

The cardiovascular system (CVS) regulation can be studied from a central viewpoint, through heart rate variability (HRV) data, and from a peripheral viewpoint, through laser Doppler flowmetry (LDF) signals. Both the central and peripheral CVSs are regulated by several interacting mechanisms, each having its own temporal scale. The central CVS has been the subject of many multiscale studies. By contrast, these studies at the level of the peripheral CVS are very recent. Among the multiscale studies performed on the central CVS data, multiscale entropy has been proven to give interesting physiological information for diagnostic purposes. However, no multiscale entropy analysis has been performed on LDF signals. The authors' goal is therefore to propose a first multiscale entropy study of LDF data recorded in healthy subjects.

METHODS

The LDF signals recorded in the forearm of seven healthy subjects are processed. Their period sampling is T=50 ms, and coarse-graining scales from T to 23T are studied. Also, for validation, the algorithm is first tested on synthetic signals of known theoretical multiscale entropy.

RESULTS

The results reveal nonmonotonic evolution of the multiscale entropy of LDF signals, with a maximum at small scales around 7T and a minimum at longer scales around 18T, singling out in this way two distinctive scales where the LDF signals undergo specific changes from high to low complexity. This also marks a strong contrast with the HRV signals that usually display a monotonic increase in the evolution of the multiscale entropy.

CONCLUSIONS

Multiscale entropy of LDF signals in healthy subjects shows variation with scales. Moreover, as the variation pattern observed appears similar for all the tested signals, multiscale entropy could potentially be a useful stationary signature for LDF signals, which otherwise are probe-position and subject dependent. Further work could now be conducted to evaluate possible diagnostic purposes of the multiscale entropy of LDF signals.