**3. Breathing pattern dynamics: physiological and pathophysiological implications**

Neurons in the brainstem govern respiratory rhythm through a network of coupled oscillators. Critical components of this network are located in a specialised region of the brainstem called the pre-Botzinger complex (pre-BotC). This complex system can generate a wide variety of rhythms [31]. Focal activation of this region has been shown to increase the frequency of inspiratory motor bursts. Del Negro and colleagues [32] showed that progressively elevating neuronal excitability of the pre-BotC of neonatal rats in vitro by increasing artificial cerebrospinal fluid K+ concentration causes periodic modulation of the inspiratory rhythm, reflected by cranial nerve XII motor discharge, in a well defined sequence of behavioural states, characterised by periodic oscillations, quasiperiodicity and ultimately disorganised aperiodic activity. In another experimental study with anesthetised adult cat models, Chen et al. [33] found that both focal hypoxia and chemical stimulation of pre-BotC can produce a marked excitation of phasic phrenic nerve discharge, characterized by high amplitude, rapid rate of rise, short duration bursts and reduced complexity, estimated with approximate entropy (low ApEn values).

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, since the respiratory pattern is created by integration of different inputs from chemoreceptors, chest wall and pulmonary receptors, the cerebrum, vagal afferents and non-respiratory central mechanisms [34,35].

Both hypercapnia and hypocapnia may alter ventilatory pattern. Jubran et al. [36] observed that hypercapnia in humans increases the gross variability of minute ventilation (MV) and VT but decreases that of inspiratory (Ti) and expiratory (Te) times. In addition, hypercapnia makes ventilation more monotonous with increased autocorrelation between adjacent values. Fiamma et al. [37] studied breath-by-breath variability and complexity of different ventilatory signals (instantaneous ventilation, tidal volume, mean inspiratory flow, inspiratory and expiratory times) in eight healthy subjects with different CO2 levels. Hypercapnia reduced breathing variability and increased all complexity indices whereas hypocapnia induced reciprocal changes. The authors concluded that chemoreceptors may exert a strong and inverse influence on ventilatory variability and complexity.

Cortical and subcortical effects upon breathing patterns dynamics are also influenced by slow-wave sleep that seems to reduce respiratory complexity [38] whereas panic-anxiety disorders may increase it [39]. Furthermore, Samon and Bruce reported that breathing complexity decreases with anesthesia and vagotomy [40].

60 Practical Applications in Biomedical Engineering

severe sepsis and septic shock [26].

estimated with approximate entropy (low ApEn values).

**implications** 

than 0.5 represent a system without any correlations, lack of memory and finally chaotic-like and unpredictable evolution in time (white noise). On the contrary, values of β slope higher than 1 or even near 1.5 characterize strong correlations within the signal and a highly predictable and almost periodic evolution in time (brown noise) [26,27]. Goldbereger [30] has studied cardiovascular dynamics in health and disease and has found that both unpredictable (random-walk) and periodic behaviors represent loss of physiologic function and correlate with lack of fractal properties of heart rate signals in patients with cardiovascular diseases. Similar results have been found also in critically ill patients with

**3. Breathing pattern dynamics: physiological and pathophysiological** 

Neurons in the brainstem govern respiratory rhythm through a network of coupled oscillators. Critical components of this network are located in a specialised region of the brainstem called the pre-Botzinger complex (pre-BotC). This complex system can generate a wide variety of rhythms [31]. Focal activation of this region has been shown to increase the frequency of inspiratory motor bursts. Del Negro and colleagues [32] showed that progressively elevating neuronal excitability of the pre-BotC of neonatal rats in vitro by increasing artificial cerebrospinal fluid K+ concentration causes periodic modulation of the inspiratory rhythm, reflected by cranial nerve XII motor discharge, in a well defined sequence of behavioural states, characterised by periodic oscillations, quasiperiodicity and ultimately disorganised aperiodic activity. In another experimental study with anesthetised adult cat models, Chen et al. [33] found that both focal hypoxia and chemical stimulation of pre-BotC can produce a marked excitation of phasic phrenic nerve discharge, characterized by high amplitude, rapid rate of rise, short duration bursts and reduced complexity,

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, since the respiratory pattern is created by integration of different inputs from chemoreceptors, chest wall and pulmonary receptors,

Both hypercapnia and hypocapnia may alter ventilatory pattern. Jubran et al. [36] observed that hypercapnia in humans increases the gross variability of minute ventilation (MV) and VT but decreases that of inspiratory (Ti) and expiratory (Te) times. In addition, hypercapnia makes ventilation more monotonous with increased autocorrelation between adjacent values. Fiamma et al. [37] studied breath-by-breath variability and complexity of different ventilatory signals (instantaneous ventilation, tidal volume, mean inspiratory flow, inspiratory and expiratory times) in eight healthy subjects with different CO2 levels. Hypercapnia reduced breathing variability and increased all complexity indices whereas hypocapnia induced reciprocal changes. The authors concluded that chemoreceptors may

the cerebrum, vagal afferents and non-respiratory central mechanisms [34,35].

exert a strong and inverse influence on ventilatory variability and complexity.

Apart from chemoreceptor signalling, chest wall and pulmonary receptors may continuously affect central neural output, especially during resistive breathing. Brack and Tobin [11] measured breathing variability over one hour in ten patients with restrictive lung disease and in seven healthy subjects. They found that variability of Ti, Te and VT, were significantly reduced in the patients group compared with the healthy group. Furthermore, autocorrelation coefficients were increased almost 3-fold in the patients group, indicating increased periodicity. According to the authors, the decreased breath-to-breath variability in restrictive lung disease patients is a compromise between increased effort and carbon dioxide clearance and arises from their voluntary control of ventilation, as they 'choose' to do it in order to reduce respiratory distress [11,41,42].

Of particular importance in the ICU setting is the potential impact of systemic inflammation on breath-to-breath dynamics as suggested by endotoxin response studies. In a clinical study of Preas and colleagues [43], 12 healthy subjects were randomized to receive endotoxin or saline. Administration of endotoxin after 3 to 4 hours increased RR, decreased Ti, produced dyspnea, augmented autocorrelation coefficients within RR time series and decreased random fraction of variational activity of frequency. These changes were related to changes in arterial carbon dioxide tension. The authors concluded that endotoxin has a direct effect on respiratory controller function whose increased output causes dyspnea. They suggested that decrease in random fraction of breath variability, meaning reduced freedom to vary the respiratory cycle, was attributed to a decrease in circulation time between the lung and the chemoreceptors, secondary to an increase in cardiac output. Since ibuprofen, a cyclooxygenase inhibitor, did not abolish dyspnea, something that seems to happen in healthy exercising subjects, the authors proposed that endotoxin augments respiratory center output through other alternative pathways [44, 45].

#### **4. Fractals and power law in pulmonary physiology**

Many organs in different biological systems have fractal structure. Fractal branching reduces the distances over which materials are transported, providing rapid and efficient delivery of nutrients [46]. The lung offers many examples of self-similarity properties. Weibel and Gomez [47] first measured the morphology of human airways and found an exponential relationship between the diameter and the generation number of the conducting airways. Mandelbrot [48], who was the first who introduced the term fractals, discovered a unifying scaling pattern of the branching in the lung. Its higher fractal dimension corresponds to a more complex branching, whereas a lower one reflects a more homogeneous structure. Moreover, regional pulmonary blood flow has been shown by Glenny to exhibit spatial and temporal fractal patterns [49]. The structure of alveolar surface has been also found to be well described by power laws, reflecting scale invariance [50]. The

probability distribution of airway opening during inspiration behaves also according to the power law [51].

Fractal Physiology, Breath-to-Breath Variability and Respiratory Diseases:

An Introduction to Complex Systems Theory Application in Pulmonary and Critical Care Medicine 63

demonstrated that lung function exhibit loss of fractal properties during severe asthma. Frey and colleagues [61] applied fractal methods to twice-daily peak expiratory flow (PEF) in asthmatic patients and showed that the β slope was reduced, whereas it become more regular with standard long-acting β2-agonist treatment and more random with short-acting β2-agonist treatment, respectively. Moreover, the authors were able to demonstrate that the higher the β exponent when a patient was not under any treatment, the larger the

improvement of his condition upon administration of long-acting β2-agonist therapy.

decreased overall structural complexity and pathologic severity of disease.

takes place in discrete steps [63-65].

diameter) [65].

In another study, Suki and co-workers [51] studied the dynamics of airway opening and crackles, using a simple mathematic model of the periphery of airway tree. Suki found that the time series of crackles emitted during airway opening follows a power law distribution. Additionally, as the crackles propagate up the tree, the sound amplitude is attenuated at successive bifurcations, whereas its distribution follows the power law. The same has been found for the time intervals of the 'jumps' by which airway resistance decreases upon lung inflation by a constant flow. In a study of Boser and colleagues [62], the fractal dimension of airways was computed using autopsy material from three groups: fatal asthma, non-fatal asthma and non-asthma controls. The authors were able to show that the average FDs of both fatal (1.72) and non-fatal asthma groups (1.76) were significantly lower than that of the third control group (1.83, p<0.05), whereas the lower fractal dimension correlated with a

Venegas and colleagues [63], using positron emission tomography (PET) imaging and computer modeling showed that in cases of bronchoconstriction and when smooth muscle activation reaches a critical level, localized clusters of poorly ventilated lung regions can develop abruptly in discrete steps. These steps are called *avalanches* and can lead to new stable conditions. Because of the fractal structure of the airways, small initial heterogeneities that are always present and particularly in the diseased lung, can be amplified, leading to sudden patches of poorly ventilated lung regions. Another implication is that since airways are organized into a fractal network embedded in the elastic parenchyma, the constriction of one airway can propagate and cause an avalanche-like constriction in large parts of the lung. The same holds true for the opposite process, where opening of airways during inhalation

Suki [51] has also demonstrated that airway opening upon inflation occur in avalanches with power law distribution of both the size and time intervals between them. The significance of these results is that the probability of finding a large avalanche is much higher than it would be if the distribution were Gaussian or exponential, so both the magnitude and timing of pressure excursions applied at the airways (i.e., using mechanical ventilation) may be critical in triggering the avalanche process of alveolar recruitment [24].

In conclusion, these studies in asthma show that when the airways are likely to approach their critical closing threshold pressure, a small stimulus can provoke a catastrophic cascade of airway closure and for that reason, there is such poor correlation between the trigger and the outcome in asthmatic patients. Moreover, the history of symptom fluctuations seems related to the structural changes of the airway tree (power law distribution of airway

Another property of fractals and power laws in pulmonary physiology is error tolerance during development. In simulations of airway morphogenesis during lung development, West [52] compared a power law branching rule with an exponential decaying one and found that in the first case, the system was less susceptible to errors introduced into the branching process. These same properties suggest that living systems are capable to operate similarly at different scales, meaning that whenever environmental conditions change they can adapt more easily to their surroundings.

Aging has been proven by Lipsitz and Goldbereger [30] to be significantly associated with loss of complexity of physiological signals, leading to decreased ability to adapt to different physiological insults. Using different algorithms for estimating fractal properties and power law behavior, these authors found that the β slope of different signals in elderly was either reduced (decreased lower than 1) or augmented (increased higher than 1) compared to younger adults, indicating chaotic or periodic behavior, respectively. Peng and co-workers [53] showed that aging was associated with a breakdown of fractal dynamics of respiratory signals via a decrease in β slope towards 0.5 (randomness). Concerning early stages of development in humans, one study [54] has found that ultrasonographic patterns for assessment lung maturity showed fractal properties with a power law behavior. In addition, the β slope increased with gestational age from 28 to 38 weeks. Szeto and co-workers [55], calculated β slopes of different respiratory signals in human fetus and showed its movement from randomness towards fractal behavior with gestational age. In conclusion, it seems that there is great variability in complexity with age in early life, after which complexity decreases with aging.
