Complexity in asthma, fluctuations in airway function and avalanches; beyond single measurements of lung function.

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1 Complexity in asthma, fluctuations in airway function and avalanches; beyond single measurements of lung function. Urs Frey, MD PhD Dept of Paediatric Respiratory Medicine, University Children s Hospital of Bern Inselspital 3010, Bern Switzerland Asthma is a chronic disease of the airways with multiple long-acting influences such as inflammation and immunological and mechanical (remodelling) mechanisms. The complex interactions between endogenous and environmental factors result in a highly variable pattern of airway obstruction over time. Fluctuations in airway calibre result in episodic symptoms of wheeze, dyspnea or cough. Long-term fluctuation in asthma can for example be seen in series of daily symptom scores or daily lung function measurements. Understanding and predicting such fluctuations is difficult not only because environmental stimuli are not always recognisable and simple to quantify, but also because the correlation between stimuli and symptoms is poor (1-4). The lack of a deterministic relationship between a stimulus and its outcome is an essential feature of complex dynamic systems. In many complex systems, these fluctuations exhibit long-range correlations which are typically scale-invariant and thus show similar statistical properties over different time scales. In the time domain, processes with scale-invariant correlation properties are called fractal processes. We have recently been shown that the day-to-day lung function fluctuations in chronic asthma exhibit fractal properties characterised by long-range correlations (5). Fractal processes may also arise when signals travel through structures which themselves have spatial fractal scaling. In this regard, it is important to note that we find fractal properties in both structure and function of the respiratory system (6-8).

2 Fractal type networks in the lung structure The three dimensional structure of the airways is a well-known example of a complex fractal structure. Fractals are self-similar structures, in which magnified subparts resemble the entire structure. With regard to the airway tree, the self-similarity is manifest in a branching pattern that repeats itself over multiple length scales. Although fractality is optimal for lung ventilation, it also shows some unexpected peculiarities in diseases. The structural organisation of this fractal network has important consequences for physiology and medicine. In a lung with small ventilation inhomogeneities, bronchoconstriction does not take place homogeneously in all airway segments. Although it has been known since the mid-1970s that the distribution of ventilatory inhomogeneities in asthma is nonhomogeneous, Venegas and co-workers (9) recently demonstrated, using positron emission tomographic imaging, that once smooth muscle activation reaches a critical level, localised clusters of poorly ventilated airways can develop abruptly in discrete steps. These steps are called catastrophic shifts or avalanches (10) and lead to a new stable condition. As a consequence of the fractal network structure, with its elastic interactions through the parenchyma, initial small ventilation inhomogeneities lead to self-organised patches of poorly-ventilated lung during bronchoconstriction. Thus, an airway cannot close or open without influencing neighbouring airways, and the constriction of a single airway has consequent effects on other airways. This study is fascinating, since it offers a new understanding of asthma attacks on a structural level. In asthma, the airways in the lung are likely to be close to the local critical closing threshold pressure, which means that a small additional stimulus can cause a catastrophic avalanche with severe impairment of lung function. Such threshold-based mechanisms are highly nonlinear in nature, which may offer an explanation for the poor relationship between trigger and outcome in asthma in general and fatal asthma attacks in particular, as noted previously.

3 Fractal type networks in the physiological times series and signals Fractal complex behaviour is not only found in structure of the lung but also in longterm time series of physiological signals generated by the lung. An example of a twice daily peak flow (PEF) series of 6 month duration is shown in figure 1. It can be seen that PEF behaviour is highly variable but not random over time. In order to analyse such PEF series, we investigated the temporal pattern in 80 asthmatic subjects (5) who had taken part in a longterm clinical trial (11). In particular, we examined whether the statistical and correlation properties of the time series of PEF recordings could be used to predict the risk of a subsequent episode of asthma. We found that the fluctuations in a series of daily PEF measurements exhibited fractal-type long-range correlations. These correlation properties of the signal can be characterised by the so called detrended fluctuation analysis (12) which measures the extent to which the average variations in the past affect the variation in the present. Often the correlation function follows a power law which allows one to characterise the complex behaviour with a simple number, α, the exponent of the power law. A value of α of 0.5 represents a random uncorrelated process; the higher α the more highly correlated is the time series and the higher degree of internal long range correlation or memory. We found that α of the PEF series was correlated to asthma severity (5). What are the consequences of these findings? In a temporal process with long-range correlations, the amplitudes of fluctuations that occurred in the past influence the current value. However, the influence of previous fluctuations decreases as the time interval increases. The value of α, and hence the strength of these long-range correlations, will be influenced by the integrative contribution of inflammation and immunological, and mechanical (remodelling) mechanisms. Thus, asthma as a chronic disease behaves as a complex nonlinear system with internal memory properties related to disease severity. The clinical surrogate for this memory in asthma embodied in the immune system, in chronic airway inflammation and in structural remodelling may be manifest as persistent bronchial

4 hyperactivity after a single allergen challenge (2), persistent symptoms following stimulus removal in occupational asthma (3) or persistent remodelling, and inflammation after clinical remission of asthma (4). Although it is impossible to disentangle all the individual components of the system and its memory properties, it is possible to describe the overall dynamic behaviour of the disease in a comprehensive, integrative manner using a systems approach. Internal long-range correlations are also important for the stability of the system. By knowing both past values of PEF, embodied in the memory (α) of the PEF series and the coefficient of variation of PEF), it is possible to calculate the probability or risk (more precisely the conditional probability) that, given the current value of PEF, a severe episode of asthma (say with a PEF of less than 60% predicted) will occur within any time period (say the next month). Using such mathematical analysis we have assessed the impact of treatment on asthma. Clinical and physiological data from a previous study (5) were obtained during three 6-month crossover treatment periods: regular short-acting β 2 -agonist, regular long-acting β 2 - agonist (salmeterol: 50 mg twice daily) and matching placebo. Interestingly, this internal memory was not altered by long-acting β 2 -agonists. However, repetitive short-acting β 2 agonists altered the correlated nature of the PEF time series such that the time series became more similar to a random process. Since a random process is less predictable, this finding has important consequences for the risk for future severe obstructive episodes. While long-acting β 2 mimetics significantly decreased this risk, regular short acting salbutamol tended to increase this risk. While short acting β 2 mimetics are the first line drug for on-demand relief of bronchial obstruction, it appears that when given regularly, they drive the internal regulation of airway tone towards a random process and make the system less stable and hence an exacerbation event significantly more likely. What is the potential general message of the latter finding? We speculate that short-acting, pulsatile or regularly given treatment might disturb the internal homeokinesis of normal airway function. It also tells us that perhaps

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