A considerable body of data suggests that healthy individuals exhibit breath-to-breath variability of breath components in a breath series [

23,

24]. Breath-to-breath variations have been traditionally treated as random uncorrelated white noise superimposed on the output of the respiratory controller [

24,

25]. According to Tobin, the random fraction aids respiratory system to perform tasks other than gas exchange, such as speaking [

26]. Only simple statistics such as mean, variance and coefficient of variation can estimate random variational fraction after averaging over many breathing cycles. Since variability in complex living systems is not only an artefact of biological noise but also an intrinsic property of various control mechanisms, different types of deterministic (non-random) variability have been described in the pattern of breathing [

27-

29].

Neurons in the brain stem govern respiratory rhythm through a network of coupled oscillators. Critical components of this network are located in a specialised region of the brain stem called the pre-Botzinger complex (pre-BotC) [

30]. Del Negro and colleagues showed that progressively elevating neuronal excitability of the pre-BotC of neonatal rats in vitro causes periodic modulation of the inspiratory rhythm, characterised by periodic oscillations, quasiperiodicity and ultimately disorganised aperiodic activity [

31]. In another experimental study with anesthetised adult cat models, Chen et al found that both focal hypoxia and chemical stimulation of pre-BotC can produce a marked excitation of phasic phrenic nerve discharge, characterized by reduced complexity, estimated with approximate entropy (low ApEn values) [

32]. The above studies support the hypothesis that central respiratory centers are responsible for different breathing patterns with various degrees of variability and complexity in different settings and levels of stimulation. In addition, they can also adapt ventilation to metabolic needs through integration of afferent information.

Apart from chemoreceptor signalling, chest wall and pulmonary receptors may continuously affect central neural output, especially during resistive breathing [

33,

34]. Brack and Tobin measured breathing variability using CVs and autocorrelation analysis, over one hour in ten patients with restrictive lung disease and in seven healthy subjects. They found that variability of inspiratory time (Ti), expiratory time (Te) and V

_{T}, were significantly reduced in the patients group compared with the healthy group [

26].

Several approaches have been used for the study of respiratory complexity. Donaldson in 8 adults during resting breathing found that different respiratory parameters were characterized by positive lyapunov exponents [

35]. Increased respiratory approximate entropy and lyapunov exponents have been reported in patients with panic disorders [

36], whereas Akey and colleagues described a reduction in respiratory ApEn upon a hypoxic insult to the brain [

37]. Peng who introduced the DFA algorithm for the study of noisy and nonstationary biological signals found that breathing intervals' DFA exponents were significantly decreased in elderly compared to young adults [

38]. Finally, hypercapnia has been found to decrease complexity but increase largest lyapunov exponents of different respiratory time series [

39].

Implementation of different mathematical tools derived from signal processing techniques for analyzing heart rate and respiratory pattern variability has been shown to provide prognostic information in the assessment of weaning readiness [

40,

7-

10]. Engoren studied 10 control patients who had undergone cardiac surgery and 21 patients who required prolonged (> 7 days) ventilatory support and found increased ApEn values of tidal volume in weaning failure subjects [

7]. However and according to a study from Caminal, an inverse relation between the level of pressure support and the CVs of different ventilatory parameters has been established, supporting the view that unloading of respiratory muscles is associated with increased breathing pattern variability, at least in weaning success patients [

41]. El-Khatib assessed 52 patients with various disorders during a continuous positive airway pressure (CPAP) trial of 5 cm H

_{2}O for 60 minutes and found that the CVs, the Kolmogorov-Sinai entropy (sum of largest lyapunov exponents) and the correlation dimension (measure of fractal-like properties) of tidal volume and airway flow were all significantly smaller in the successfully weaning group compared with the failure weaning group [

8]. On the contrary, Bien and Wysocki reported decreased variability of different ventilatory parameters in weaning failure patients [

9,

10]. However, they did not perform non-linear analysis of respiratory time series for assessing breathing complexity. In another interesting study, Vallverdu and colleagues examined heart rate and respiratory pattern complexity in 78 patients during weaning trials using information flow analysis, which describes the regularity of signals by estimating the auto- and mutual information functions. The authors were able to find reduced complexity and a more coupled nonlinear oscillator behavior in weaning failure subjects [

42].

To our knowledge, this is the first study in medical literature that applied a 'toolkit' of nonlinear methods in respiratory signals for estimating weaning outcome, in a cohort of surgical patients. In a recently published study that included a similar group of patients and implemented the same weaning protocol, we found reduced complexity and coupling of heart and respiratory rate signals derived from bedside monitors and estimated with DFA and different entropy metrics, in subjects who failed to separate from the ventilator [

43]. However, since description of ventilatory complexity requires the assessment of both predictability (entropy) and sensitivity to initial conditions (Lyapunov exponents) of continuous oscillatory signals (flow) and time series of discrete values [

24], we decided to apply these methods to different respiratory signals derived from the ventilator. In addition, we tried to assess their scale-invariant properties by computing the fractal dimension. Finally, we applied the DFA algorithm for quantifying fractal properties of respiratory signals through the estimation of long-range correlations, which contrary to fractal dimension, is more suitable for analyzing non-stationary short time series. In conclusion, we assumed that the implementation of different methods for the mathematical description of respiratory complex dynamics that was not performed in our previous report (except for sample entropy), could add significant value in such analysis, in case of significant differences between patients with different outcome of interest. We used the same weaning protocol as Bien, who examined a sample of 78 patients with systemic inflammatory response syndrome (SIRS) [

9].

All indices of respiratory complexity were found to exhibit inverse changes between weaning failure and success groups. After the performance of a SBT, increased unloading of the respiratory system was associated with increased breathing complexity in subjects who managed to liberate from the ventilator (figures ), since lower values of DFA exponent and higher values of LLE and SampEn of inspiratory flow were found (figure ). These results indicate reduced long-range correlations, increased sensitivity to initial conditions and augmented irregularity of flow. Tidal volume signals exhibited similar changes in DFA and LLE without reaching statistical significance, whereas fractal dimension of both signals increased insignificantly in the weaning success group. In conclusion, our findings support the hypothesis that increased ventilatory randomness was associated with weaning success and proved to be more reliable in discriminating patients with different weaning outcome in relation with conventional indices (figure ). Moreover, ventilatory complexity must be estimated with a combination of nonlinear techniques, since respiratory time series are often very noisy and highly nonstationary, compared with cardiovascular signals [

38,

43].

These results parallel those from Schmidt and colleagues who reported increased LLE and Kolmogorov-Sinai entropy values of mean inspiratory flow signals in mechanically ventilated patients, after switching the ventilator from the pressure support mode to neurally adjusted ventilatory assist mode (NAVA) [

44]. According to these authors, successful spontaneous breathing trials unmask underlying variability and complexity of central neural output, since inspiratory pressure inhibits the respiratory drive. This effect is nicely reflected through the increased complexity indices of flow and is responsible for better neuro-mechanical coupling.

In another study, Mangin and colleagues investigated ventilatory chaotic dynamics in 17 mechanically ventilated patients during switching the ventilator from the assist-control mode to pressure support mode [

45]. They were able to show that both fractal dimension and LLE were increased, particularly in 5 patients who were successfully extubated. Furthermore, the authors supposed that increased breathing complexity may also be attributed to higher vagal afferent feedback during unassisted breathing, as has already been shown by Sammon and Bruce [

46].

These studies support our findings that transition between mechanical and spontaneous ventilation is associated with increased complexity of respiratory signals in weaning success patients, since duration of ventilation before the SBTs was similar between groups with different weaning outcome. Moreover, in a study of Burykin and Buchman investigating cardiorespiratory dynamics and synchronization during controlled and unassisted breathing in 13 surgical patients, it was demonstrated that mechanical ventilation reduces significantly both heart and respiratory rate complexity whereas spontaneous respiration is more irregular with increased uncoupling of cardiorespiratory rhythms in weaning success patients [

47].

Higher variability and complexity of breathing pattern during controlled ventilatory support has been found to ameliorate oxygenation. In an oleic acid injury animal model, Mutch introduced fluctuations according to an algorithm, to mechanical respiration and found increased respiratory arrhythmia and oxygenation and decreased dead space compared with conventional ventilation (with similar MV) [

48]. According to Suki, when fluctuations in the form of symmetrically distributed random noise is added to peak airway pressures, the mean does not change but isolated values can be augmented, leading to significant alveolar recruitment [

49]. Moreover, low respiratory variability during both controlled and unassisted breathing could deteriorate respiratory mechanics by promoting microatelectasis [

10].

Reduced respiratory complexity of flow signals in group U related to group S and between the two phases of PS within weaning failure patients might also reflect loss of effective control mechanisms that govern respiratory rhythms through a network of coupled oscillators [

50]. It seems that increased respiratory load reduces complexity of central oscillator output, as it has been suggested from the different studies discussed so far. Moreover, Preas in a clinical study estimating endotoxin effect upon respiratory variability and complexity found a decrease in RR random variability in patients with restrictive lung diseases, a similar pattern of change with Tobin's study [

26] and attributed dyspnoea to the endotoxin effect upon brain stem neurons [

51]. In our study, the majority of weaning failure patients exhibited dyspnoea and rapid shallow breathing, whereas most of them had high APACHE II scores upon admission. Their characteristics parallel those of the Bien's study, implying the possible presence of SIRS during the weaning trials.

Furthermore, we assume that the observed significant results in different complexity properties for inspiratory flow and not for tidal volume in weaning failure patients could also be attributed to the decreased random variability of RR, which was found in Preas and Tobin's studies. According to Bruce, any respiratory activity includes variability of different types, such as random correlated and uncorrelated, periodic and nonlinear deterministic [

24]. Alterations in the random fraction, although not measured in our study, could affect the reliable mathematical description of the non-random one, something that might limit the relevance of these results [

24].

For that reason, different techniques, such as the noise titration method, have been implemented for detecting chaotic dynamics [

45,

52]. However, in this study we did not adopt this technique, since our aim was not to detect the existence of ventilatory chaos but to investigate possible alterations in respiratory dynamics after a specific intervention (SBT). Moreover, we recruited a homogeneous group of patients and it is reasonable to assume that there were no intersubject variations at the level of noise.

Our study suffers several other limitations due to small sample size, which could increase false negative results and be responsible for lack of statistical significance in different non-linear properties of ventilatory signals. In addition, implementation of sophisticated mathematical techniques remains a challenge for average physicians, whereas their standardization is urgently needed, since there is a lack of guidelines for parameter choice and bias to low values, in some cases. Concerning methodological issues, non-linear characterization methods are extremely sensitive to noise and biased when applied to short data sets [

24,

28]. Another important issue concerns non-filtering of signals, since it has been proven that using filters can distort the characterization of non-linearities [

53]. Finally, using low sampling frequency avoids introduction of linearities within the time series, which has been found to occur during oversampling [

53].

In conclusion and despite the fact that inspiratory flow and V_{T }time series preserved their fractal-like properties, weaning failure patients exhibited reduced breathing pattern complexity during weaning trials, compared with subjects who were successfully separated from the ventilator. Increased respiratory load due to unresolved inflammatory response could be responsible for reducing effective neuro-mechanical coupling. The fact that multiplying the methods and studied parameters did not increase the chance of getting significant results for both flow and tidal volume could be associated with inherent limitations of such methods applied to short and highly noisy time series, patient characteristics or possible presence of unknown covariates. For that reason and based on findings form this and our previous study, we believe that a multimodal monitoring using in addition, both cardiovascular and electroencephalographic signals might increase diagnostic accuracy of such approach. Furthermore, the implementation of other methods such as information flow could be more suitable for studying the highly noisy and nonstationary ventilatory signals. Finally, a comparison between nonlinear properties of heart and different respiratory time series for predicting weaning outcome could shed more light into complex cardiorespiratory interactions during weaning trials.