Sci. Aging Knowl. Environ., 21 April 2004
Vol. 2004, Issue 16, p. pe16
[DOI: 10.1126/sageke.2004.16.pe16]


Physiological Complexity, Aging, and the Path to Frailty

Lewis A. Lipsitz

Lewis A. Lipsitz is at the Hebrew Rehabilitation Center for Aged, Beth Israel Deaconess Medical Center, and Harvard Medical School, Boston, MA 12131, USA. E-mail: Lipsitz{at}

Key Words: complexity • variability • fractal • power law • heart rate • frailty


Over the past decade, clinicians and investigators have begun to recognize frailty as a distinct geriatric syndrome associated with a high rate of morbidity and mortality, and therefore deserving of rigorous investigation (see Walston Perspective). Frailty has been characterized in numerous ways, including as (i) a wasting syndrome; (ii) a physiological state of vulnerability to increased morbidity and mortality (1); (iii) a constellation of signs and symptoms that include weight loss, decreased activity, muscle weakness, fatigue, and slow gait (2); (iv) a loss of physiological reserve; and (v) altered homeostatic capacity (3). By defining a phenotype of frailty and using it in their clinical research, Fried and colleagues have been able to describe several pathophysiological abnormalities and adverse outcomes associated with frailty (see "Dying of Old Age") (2); however, its underlying mechanisms remain poorly understood. Because frail individuals often have multiple age- and disease-related impairments that limit their ability to meet the demands of everyday life, frailty can be viewed as a manifestation of the degradation of multiple physiological systems that are normally responsible for healthy adaptation to daily stresses.

Normal physiological function requires the integration of complex networks of control systems, feedback loops, and other regulatory mechanisms to enable an organism to perform a variety of activities necessary for survival. The control systems of the human body exist at molecular, subcellular, cellular, organ, and systemic levels of organization, and operate over multiple time scales. Continuous interplay among the electrical, chemical, and mechanical components of these systems ensures that information is constantly exchanged, even as the organism rests. These dynamic processes are evident in the complex variability of physiological control systems, such as blood pressure (BP), heart rate (HR), brain electrical activity, gait, balance, and hormone concentrations, when they are measured on a moment-to-moment or beat-to-beat basis. (It is important to measure the continuous behavior of these systems, rather than their average value over some time period, to detect the dynamics.) Complex physiological dynamics enable an organism to rapidly respond to internal and external perturbations. Previous work, described below, indicates that aging and disease are associated with a loss of complexity in the dynamics of many integrated physiological processes. This phenomenon is evident in the continuous HR (called a HR time series) of a young person and an elderly person shown in Fig. 1. The average HR and standard deviation of HR are almost identical in these people, but their dynamics appear to be very different and can be quantified by a measure of complexity: approximate entropy (4).

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Fig. 1. HR time series for a healthy young person (top panel) and an elderly person (bottom panel). The mean and standard deviation of HR are nearly identical, but the dynamics are very different. The statistic "approximate entropy" was used to quantify the irregularity of these time series. [Reprinted with permission from (37)]

In this Perspective, we provide evidence for the degradation of physiological systems with age and disease, and we propose that the loss of adaptive capacity that ensues might characterize the syndrome of frailty. We conclude with recent preliminary evidence that age- or disease-related functional impairments might be reversible with interventions such as exercise that can restore healthy dynamics in multiple physiological systems (see, for example, "A Walk a Day Keeps the Brain OK").

The Measurement of Complex Dynamics

Recently, a variety of measures derived from the fields of nonlinear dynamics and statistical physics have been developed to describe the dynamics of physiological systems. These measures have been used to distinguish healthy function from disease and to predict the onset of adverse health-related events (5). Many of these are based on the concept of fractals.

The classic definition of a fractal, first described by Mandelbrot (6), is a geometric object with "self-similarity" over multiple measurement scales (Fig. 2). For example, the ragged, irregular appearance of a coastline or cloud looks similar whether it is measured in inches, feet, or miles. The branching structures of tree limbs or lightening bolts also demonstrate self-similarity (Fig. 2), as do the respiratory tree, circulatory system, and nervous system of higher organisms. The smaller the measuring device, the larger the length of a fractal object. This is a property known as "power-law scaling."

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Fig. 2. Fractal objects in nature. Lightning bolts and clouds demonstrate self-similarity on multiple measurement scales. [Credit: National Oceanic and Atmospheric Administration (Department of Commerce) Photo Library, National Severe Storms Laboratory Collection]

The outputs of dynamic physiological processes such as HR, which are measured over time rather than space, also have fractal properties (7) (Fig. 3). Their fluctuations appear self-similar when observed over seconds, minutes, or hours. Furthermore, they demonstrate power-law scaling in the sense that the lower the frequency of oscillation of these signals, the larger their amplitude (amplitude squared is "power").

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Fig. 3. Examples of spatial self-similarity in a branching structure such as the respiratory tree or circulatory system (left), and temporal self-similarity in a physiological process such as beat-to-beat HR (right). HR fluctuations look similar whether they are plotted over 300, 30, or 3 min. This property resembles a fractal process. [Reprinted with permission from (49); Copyright (2002) National Academy of Sciences, U.S.A.]

This inverse power-law relation can also be expressed as the equation shown in Fig. 4. Taking the logarithm of each side of this equation yields a linear relation between amplitude and frequency (f), the slope of which is the scaling exponent {beta}. Any process with 1/f or power-law scaling is fractal-like.

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Fig. 4. The inverse power-law relation. In this equation, A = amplitude, f = frequency, and {beta} is the scaling exponent.

Physiological signals, such as fluctuations in HR, respiration, and walking in healthy people, are good examples of fractal processes, because their fluctuations on short time scales are similar to those on longer time scales. Fractal scaling has been observed in these complex signals, indicating the presence of long-range (power-law) correlations in the underlying dynamics (8, 9). These long-range correlations appear to be a dynamical hallmark of healthy integrative control systems. Over the past several years, a number of studies discussed below have demonstrated that the fractal properties of physiological signals degrade with aging and disease and can serve as predictors of adverse outcomes (10-20).

An inherent problem in the detection of fractal scaling in "real-world" physiological signals is the presence of "nonstationary" trends in the data: trends that are a result of measurement noise, artifacts, and other nonphysiological influences. To overcome this problem, Peng and colleagues developed a method termed detrended fluctuation analysis (DFA) (11, 21) to assess the fractal properties of physiological time-series data. The advantages of DFA over conventional two-point correlation methods (for example, spectral analysis and Hurst analysis, which are standard engineering and math analyses) are that it permits the detection of long-range correlations embedded in a seemingly nonstationary time series, and also avoids the spurious detection of apparent long-range correlations that are an artifact of nonstationary trends. This method has been validated on a control time series that consists of long-range correlated data superimposed on a nonstationary external trend (21). This method has also been used successfully to detect long-range correlations in highly complex heartbeat time series (11, 14, 22, 23) and other physiological signals (24-26).

Recently, an algorithm called multiscale entropy analysis (MSE) was also developed to quantify the complex dynamics of physiological signals (27, 28). The detailed mathematical algorithm to compute MSE can be found in the original publication (28). The algorithm combines two concepts to define complexity: (i) a fundamental concept originating in statistical physics and information theory, called entropy; and (ii) the idea that a fractal biological system does not exhibit a characteristic time scale. In preliminary studies, MSE could discriminate HR dynamics in young people, elderly people, and heart-failure patients with 92% accuracy (28). In contrast, traditional methods that focus only on single-scale measurements could not distinguish between these three groups.

It is important to recognize the difference between "complexity" and "variability." A high-amplitude sine wave is highly variable but minimally complex, because it has only one scale of measurement and can be described mathematically by a simple periodic function. In contrast, a low-amplitude signal with fractal-like long-range correlations (self-similarity over multiple scales) is less variable but highly complex, requiring an aperiodic nonlinear function to describe it. With aging or disease, some processes such as HR lose both complexity and variability (23), whereas others, such as beat-to-beat blood pressure (29) or stride interval during walking (26), become more variable but less complex.

Origin of Complex Dynamics in Physiology

As a result of the availability of electrocardiographic and BP monitoring devices in medical practice, cardiovascular dynamics are probably the most intensively studied dynamics in humans. The sympathetic and parasympathetic limbs of the autonomic nervous system (the part of the nervous system that is not under conscious control) account for most of the short-term (second-to-second) beat-to-beat variability in HR and BP. On longer time scales of minutes to hours, hormonal and temperature influences regulate HR and BP, whereas over 24-hour-periods, circadian rhythms exert their control. The importance of the autonomic nervous system in beat-to-beat cardiovascular variability is evident from pharmacological blocking studies. During blockade of the parasympathetic and sympathetic nervous systems with atropine and propanolol, respectively, beat-to-beat HR fluctuations are attenuated (Fig. 5). Yamamoto and colleagues have shown that blockade of the vagus nerve (which innervates the heart and gut) with atropine decreases the fractal nature of HR variability (30).

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Fig. 5. Loss of complex HR fluctuations during autonomic blockade with atropine and propanolol.

Our previous study of the maturation of sympathetic innervation to the heart during the first month of life in neonatal swine provides another example of the influence of the autonomic nervous system on HR variability and supports the idea that sympathetic innervation contributes to HR complexity (31). As sympathetic neurons from the right stellate ganglion (a group of nerve cell bodies located in the region of the neck) sprout connections to the heart during this time period, baby pigs develop increasing complexity in their HR time series (Fig. 6). When the stellate ganglion is denervated at birth, the animals fail to develop the HR irregularity that is characteristic of mature animals.

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Fig. 6. The increasing complexity of HR as baby pigs develop sympathetic innervation of the sinus node of the heart (the region that produces cardiac impulses) from the stellate ganglion during the first 30 days of life. Note the emergence of complex HR dynamics, quantified by increases in the value of the statistic approximate entropy (ApEn). R-R interval, the time between each beat. [Reprinted from (31) with permission from Elsevier]

Similarly, Kresh and Israiltyan have shown that the transplanted human heart develops increasing complexity of HR variability after implantation (32). This dynamic reorganization in the allograft rhythm-generating system probably represents the emergence of local intracardiac control mechanisms, followed by systemic hormonal and neural inputs that evolve over the course of graft-host adaptation.

The tremor displayed by individuals with Parkinson's disease (PD) provides additional support for the notion that complex dynamics are the result of integrated control networks. In PD, neurons that produce the neurotransmitter dopamine are lost from the substantia nigra, a small region of the brain near the brainstem. In healthy individuals, these dopaminergic neurons form connections with neurons in the striatum, a region of the midbrain that controls movement, and modulate their activity via the release of dopamine (see Andersen Review). The normal output of this rich interconnected network of neurons within the substantia nigra and striatum produces an irregular, low-amplitude, aperiodic physiological tremor that is evident when one's hand or foot is held in a resting position. Edwards and colleagues (33) developed a model of the neural network of dopaminergic innervation in the nigro-striatal pathway of the brain to produce a time series characteristic of the normal physiological tremor. Using this model, they showed that parameter changes representing weakened synaptic connections due to loss of dopamine result in the emergence of a periodic tremor resembling that of PD (33). This loss of complexity through "dynamic simplification," as they call it, not only suggests potential mechanisms that underlie the complex output of the motor control system but also demonstrates how the disconnection of interacting pathways in the central nervous system might be associated with the development of PD.

Functional Implications of Complex Dynamics: Promoting an Adaptive Response to Stress

The complex dynamics underlying healthy physiological control systems probably serve an important purpose: They enable an organism to mount a focused adaptive response in order to perform a specific task or overcome an external stress. Therefore, baseline system complexity should predict one's ability to mount a response. Because the response is by definition singular and directed at overcoming a stress, it should be less complex than the baseline condition. There are several lines of evidence that support this notion.

In a recent study of young, young-old, and old-old humans, Vaillancourt and Newell (34) examined the complexity of the force output of the first finger while study participants were generating a constant force (baseline condition) or tracking a sine wave target (adaptive task). Under baseline conditions, a variety of complexity measures (DFA, approximate entropy, and 1/f slopes) showed reduced complexity as a function of age. However, during the task, complexity became lowest in the young (indicating accuracy in tracking the target), was slightly lower in the young-old group, and remained unchanged in the oldest group. Therefore, participants with the greatest baseline complexity had the greatest ability to perform an adaptive task.

Our previous work in BP dynamics provides another example of an age-related reduction in complexity and its functional implications. In the supine resting state, BP oscillations produce a broad-band frequency spectrum with fractal (1/f) properties. When a healthy young person is tilted upright to mimic standing, the BP frequency spectrum becomes less complex, giving rise to low-frequency "Mayer waves" with a dominant frequency at about 0.1 Hz (35). This low-frequency BP oscillation is thought to result from activity of the baroreflex negative feedback system, which functions to offset short-term changes in BP. In this situation, the system counters the reduction in venous return to the heart that occurs when the person is tilted upright through sympathetic nerve activation and vasoconstriction, and prevents BP overshoots through sympathetic withdrawal and vasodilation. This feedback mechanism keeps BP in the range necessary to ensure adequate organ perfusion. Many elderly people have less complexity of HR and BP dynamics in the supine resting position (29) as compared to younger people. Moreover, we have shown that elderly people often fail to develop low-frequency (baroreflex-mediated) systolic BP oscillations when tilted upright (36). This impairment might be associated with dangerous drops in blood pressure or with fainting, which can occur in elderly people when they stand up, eat a meal, or take certain medications. These observations suggest the need for further research to determine whether complex fractal-like processes have evolved in biological systems to permit an efficient adaptive response that can rapidly restore the organism to physiological stability during the exigencies of everyday life.

Loss of Complexity in Aging and Disease: The Pathway to Frailty

Lipsitz and Goldberger (37) have suggested that normal human aging is associated with a loss of complexity in a variety of fractal-like anatomic structures and physiological processes. This loss of complexity is manifest as degradation in fractal scaling (for example, breakdown in bone trabecular architecture or loss of 1/f scaling of cardiac interval time series); narrowing of a frequency response (for example, loss of the ability to hear high-frequency sounds); loss of long-range correlations in time series data (for example, cardiac interval, BP, or stride interval time series); increased randomness or stochastic activity (for example, cardiac intervals or postural sway trajectories); or greater periodicity [for example, slow, regular, electroencephalographic waves (electrical activity produced by the brain)]. Using a variety of measures that employ fractal analysis, aging has been shown to be associated with a loss of complexity in BP (29), respiratory cycle (10), stride interval (26), and postural sway dynamics (38).

Not only aging but disease results in a loss of complexity. Common examples include the tremor of PD, the Cheyne-Stokes respiration of heart failure (rhythmic waxing and waning of respiration followed by periods when breathing stops), the periodic breathing of high-altitude sickness, electroencephalographic spike waves of epilepsy, the emotional cycling of manic-depressive illness, periodic oscillations of leukocyte counts in leukemia, and the regular rhythm of ventricular tachycardia (a life-threatening rapid HR) (7). A loss of fractal organization has been shown to be a predictor of adverse outcomes in a variety of physiological systems, including cardiac interval or stride interval time series. Heart failure and ischemic heart disease are associated with a loss of long-range fractal-like correlations in HR, and this loss of complexity is associated with increased cardiovascular mortality (14). Elderly fallers have significant increases in stride variance and reduced long-range fractal correlations in their stride-stride intervals (18). Hormones such as melatonin or insulin will not function normally unless secreted in a pulsatile fashion (39-41). Thus, normal physiological function appears to depend on complex underlying dynamics.

The unfortunate final common pathway of aging or multisystem disease is the loss of adaptive capacity and ultimate decline in functional independence that characterizes frailty. Fig. 7 illustrates how a loss of complexity might lead to frailty. In health, a rich fractal-like network of multiple interacting biological inputs results in a complex output, characteristic of an organism with high functionality that can readily adapt to the stresses of everyday life. As age or diseases reduce the number and/or connectedness of these inputs, the spontaneous (free-running) output signal is simplified. This loss of fractal complexity may be manifest by greater periodicity (the emergence of a characteristic scale) or increased randomness (the loss of long-range fractal correlations). Consequently, functional capacity is reduced. As system complexity falls further, functional capacity ultimately crosses a "frailty threshold," resulting in marked vulnerability to injury, disease, and finally death. For this reason, frail elderly individuals are particularly vulnerable to falls, confusion, incontinence, and functional dependency when exposed to common environmental, pharmacological, or emotional stresses.

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Fig. 7. Illustration of how a reduction in physiological inputs and their connections over time leads to a loss of complexity in the output signal and an associated loss of functional ability. When functional level falls below a "frailty threshold," the individual can no longer adapt to internal or external stresses and frailty ensues. [Reprinted with permission from (50); permission was granted via the Copyright Clearance Center]

Fortunately, there is considerable redundancy in many biological systems in a healthy organism; for example, humans have far more muscle mass, neuronal circuitry, renal nephrons, and hormonal stores than are needed to survive (see Gavrilov Review). This physiological reserve allows most individuals to compensate effectively for age- and disease-related changes. Because the network structure of physiological systems also enables alternate pathways to be used to achieve the same functions, physiological changes that result from aging alone usually do not have much impact on everyday life. Accordingly, otherwise healthy individuals who suffer from a single organ injury such as a stroke may regain functional capacity if other neural components and their connections can compensate. This forms the rationale for the restoration of health through a variety of interventions that promote the development of new network connections.

Restoring Healthy Dynamics

There are at least three types of interventions that could potentially restore healthy dynamics in biological systems and thus improve functional health or prevent the onset of frailty. These include (i) multisystem interventions that have effects on multiple systems (for example, exercise, Tai Chi, medications, or hormones); (ii) multifactorial interventions that identify and treat different risk factors that contribute to disease and disability [for example, multifactorial interventions for falls (42) or delirium (43)]; and (iii) external control devices and procedures that have direct effects on system dynamics [for example, pulsatile hormone infusions (39), variable end-expiratory pressure during artificial ventilation (44), and use of special pacemaker programs to terminate cardiac arrhythmias (45)].

One of the most widely studied single interventions to improve functional ability is exercise. A recent study by Tulppo et al. (46, 47) showed that 8 weeks of a moderate or high-volume aerobic exercise training program decreased the short-term scaling exponents of HR, indicating increased fractal-like correlations in the data. In another study by Hausdorff et al. (48), gait dynamics were assessed in 67 older men and women with functional impairment, randomized to a 6-month multimodal exercise intervention or attention control group. A composite gait instability index and the inconsistency of stride time variance--two measures of stride time fluctuation dynamics--improved in the exercise group but not in the control group. Thus, exercise appears to be a powerful intervention capable of restoring complex dynamics in multiple physiological systems.


Aging and disease are associated with a progressive loss of complexity in the fractal architecture of anatomical structures and dynamics of physiological processes, leading to a decline in adaptive capacity and ultimately the development of frailty. A variety of measures derived from fractal analysis can be used to quantify physiological complexity and its decline over time. These measures might be useful as predictors of adverse outcomes. Preliminary data suggest that several interventions, particularly aerobic and resistance exercise, can partially restore the complex dynamics of physiological systems and might be able to prevent or slow the onset of frailty.

April 21, 2004
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  51. Supported by National Institute on Aging grants AG04390 and AG08812. L.A.L. holds the Irving and Edyth S. Usen and Family Chair in Geriatric Medicine at the Hebrew Rehabilitation Center for Aged.
Citation: L. A. Lipsitz, Physiological Complexity, Aging, and the Path to Frailty. Sci. Aging Knowl. Environ. 2004 (16), pe16 (2004).

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