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AGING AS A PROCESS OF COMPLEXITY LOSS

Lewis A. Lipsitz, MD

In: Complex Systems Science in Biomedicine

Deisboeck, Kresh, and Kepler, editors.

Kluwer Academic Publishers, 2003

From: The Hebrew Rehabilitation Center for Aged,

Beth Israel Deaconess Medical Center,

and Harvard Medical School, Boston MA

Address correspondence to:

Lewis A. Lipsitz, MD

Hebrew Rehabilitation Center for Aged

1200 Centre Street, Boston, MA 02131

Phone: 617-363-8318, Fax: 617-363-8929

E-mail: Lipsitz@mail.hrca.harvard.edu

Supported by Grants AG04390 and AG08812 from the National Institute on Aging, Bethesda,

MD. Dr. Lipsitz holds the Irving and Edyth S. Usen and Family Chair in Geriatric Medicine at

the Hebrew Rehabilitation Center for Aged.

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INTRODUCTION

Classical research in the field of aging has been largely reductionistic, defining the

process of aging as a linear decline in many organs and physiologic systems until functional

disability results (Figure 1) (1). However, the process of aging is a nonlinear, multi-dimensional

process that is associated not only with changes in individual systems, but probably more

importantly, alterations in the connections and interactions between system components. The

complex mechanisms by which these components interact to enable an organism to perform a

variety of functions necessary for survival, is the subject of physiology.

Healthy physiologic processes require the integration of complex networks of control

systems and feedback loops that operate on multiple scales in space and time (2). For example,

physiologic systems exist at molecular, subcellular, cellular, organ, and systemic levels of

organization. Continuous interplay between the electrical, chemical, and mechanical components

of these systems ensures that information is constantly exchanged, even as the organism rests.

These dynamic processes give rise to a highly adaptive, resilient organism that is prepared to

respond to internal and external perturbations.

Recognition of the dynamic nature of regulatory processes challenges the concept of

homeostasis, which is taught by physiologists as a function of all healthy cells, tissues, and

organs to maintain static or steady-state conditions in their internal environment (3). However,

with the introduction of techniques that can acquire continuous data from physiologic processes

such as heart rate, blood pressure, nerve activity, or hormonal secretion, it became apparent that

these systems are in constant flux, even under so-called steady-state conditions. Dr. Eugene

Yates introduced the term homeodynamics to convey the fact that the high level of bodily control

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required to survive depends on a dynamic interplay of multiple regulatory mechanisms rather

than constancy in the internal environment (4).

Although it is often difficult to separate the effects of aging from those of disease and

lifestyle changes such as reduced physical activity, healthy aging in the absence of such

confounding factors appears to have a profound impact on physiologic processes. Because of the

progressive age-related degeneration of various tissues and organs, and the interruption of

communication pathways between them, complex physiologic networks break down, become

disconnected, and lose some of their capacity to adapt to stress.

There is considerable redundancy in many of the biologic and physiologic systems in

higher organisms; for example, humans have far more muscle mass, neuronal circuitry, renal

nephrons, and hormonal stores than are needed to survive. This creates a physiologic reserve that

allows most individuals to compensate effectively for age-related changes. Because the network

structure of physiologic systems also enables alternate pathways to be used to achieve the same

functions, physiologic changes that result from aging alone usually do not have much impact on

everyday life. However, these changes may become manifest at times of increased demand,

when the body is subjected to high levels of physiologic stress. For this reason, elderly

individuals are particularly vulnerable to adverse events such as falls, confusion, and

incontinence when exposed to environmental, pharmacologic, or emotional stresses.

MEASURES OF COMPLEXITY LOSS

With the development of monitoring devices that can measure the output of regulatory

processes on a moment-to-moment basis, it has become apparent that the dynamics of many

systems lose complexity with advancing age (5). The continuous heart rate time series of a

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healthy young subject and healthy elderly subject shown in Figure 2 provides a good example.

The average heart rate over the 8-minute period of recording is 64.7 beats per minute in the

young subject and 64.5 in the older subject; nearly identical. Furthermore, the standard deviation

of the heart rate is also nearly identical; 3.9 in the young subject and 3.8 in the elderly subject.

However, it is apparent that the dynamics of the heart rate time series are strikingly different.

Until recently, scientists have lacked the tools to describe these dynamics. However, new

advances in the fields of nonlinear dynamics, chaos theory, and complex systems have provided

new ways to quantify the aging process and understand its mechanisms. One particularly useful

concept that can be used to quantify the complexity of various anatomic structures or physiologic

processes is the concept of fractals.

The classic definition of a fractal, first described by Mandelbrot (6), is a geometric object

with “self-similarly” over multiple measurement scales. For example, many anatomic structures

demonstrate self-similarity in their structures and have fractal properties. The branches upon

branches upon branches of bronchi in the respiratory tree (7) or smaller and smaller vessels in the

circulatory system (8) look similar whether they are measured in microns, millimeters,

centimeters, or meters. In fact, the smaller the measuring device, the larger the length of a fractal

object. This is a property known as “power law scaling”. The output of dynamic physiologic

processes such as heart rate, which are measured over time rather than space, also have fractal

properties (9). Their oscillations appear self-similar when observed over seconds, minutes, hours,

or days. Furthermore, they demonstrate power-law scaling in the sense that the smaller the

frequency of oscillation of these signals, the larger their amplitude or “power”.

The heart rate time series demonstrates complex irregularity that has been described as a

fractal process because it looks similar whether it is plotted over days, hours, or minutes. In fact,

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the heart rate time series has “1/f” or power law scaling, in that the amplitude of oscillations (A)

is proportional to the inverse of oscillation frequency, according to the formula: A ≅ 1/fβ. The

exponent β can be derived from the slope of the log – log transformation of the Fourier power

spectrum. A fractal process (most complex) has a slope of 1, while a loss of complexity occurs as

the slope approaches 0 (white noise) or 2 (Brownian noise). The presence of 1/f fractal scaling

indicates that there are long-range (power-law) correlations in the data.

Unfortunately, the computation of the power spectrum using Fourier analysis requires

stationary data, which most physiologic signals are not. Another particularly useful technique

that minimizes the effect of non-stationarities in the data is “detrended fluctuation analysis”

(DFA), which has been well validated in a number of dynamic systems (10). The DFA algorithm

is a two-point correlation method that computes the slope of the line relating the amplitude of

fluctuations to the scale of measurement, after detrending the data. The root-mean-square

fluctuation of the integrated and detrended data are measured in observation windows of

different sizes then plotted against the size of the window on a log-log scale. The slope of the

regression line which relates log-fluctuation to log-window size quantifies the complexity of the

data (1=fractal, 0.5=random, 1.5=random-walk).

Other indicators of complexity loss in physiologic systems include an increase in

periodicity (e.g., the tremor of Parkinson’s disease), increased randomness (e.g., atrial fibrillation

of the heart), and loss of long-range correlations (e.g., gait dynamics).

It is important to recognize that complexity and variability are not the same. For

example, a high amplitude sine wave signal is quite variable, but not at all complex.

Alternatively, an irregular low amplitude signal such as the heart rate of a healthy young subject

shown in Figure 2 can be quite complex but much less variable. Similarly, irregularity and

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complexity are not the same. Traditional entropy-based algorithms such as Approximate

Entropy (11), that are used to quantify the regularity of a time series, indicate greater irregularity,

which has been interpreted as greater complexity, for certain uncorrelated random signals

associated with pathologic processes. However, as highlighted by the recent work of Costa et.

al. (12), these algorithms fail to account for the multiple time scales over which healthy

physiologic processes operate. By calculating the entropy of heart rate dynamics over multiple

time scales (multiscale entropy analysis), these investigators were able to distinguish healthy

from pathological (e.g., atrial fibrillation and congestive heart failure) dynamics, and showed

consistently higher multiscale entropy values for dynamic processes with long-range (1/f-type)

correlations, compared to those with uncorrelated random noise. Therefore, this measure appears

useful for quantifying the complexity of a time series and distinguishing it from irregularity due

to uncorrelated noise.

EXAMPLES OF COMPLEXITY LOSS WITH AGING

There are numerous examples of the progressive loss of complexity in the fractal

architecture of anatomic structures and the dynamics of physiologic processes with advancing

age. As shown in Table 1, structures such as neurons, bone trabeculae, kidney glomeruli, and

elastic fibers or dermal papillae beneath the skin all lose structural complexity with aging (5).

The loss of connectivity in bone trabeculae, which is characteristic of osteoporosis, is shown in

figure 3. Not only anatomic structures, but also physiologic processes lose complexity with

advancing age. These include heart rate (13), blood pressure (13), and respiratory dynamics (14),

center of pressure trajectories when measured on a balance platform (Figure 4), and gait

dynamics (15)(Table 2). Moreover, complexity loss has been shown to be associated with a

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variety of diseases and adverse outcomes (Tables 3 and 4). On the basis of these observations,

we have hypothesized that the age-related loss of complexity in physiologic systems, results in

an impaired ability to adapt to stress and the ultimate development of disease and disability (2).

In response to a given stress or perturbation, physiologic systems mount a specific

adaptive response that restores the organism to a new dynamic equilibrium. Therefore, the

dynamics observed during resting and stimulated conditions are often quite different. For

example, when glucose is ingested, insulin is secreted in pulsatile fashion in order to promote

glucose metabolism. When an individual stands up, blood pools in the lower extremities, and

blood pressure suddenly falls. In response, the sympathetic nervous system secretes

norepinephrine to restore the blood pressure to its resting state. Thus, the complex dynamics

observed during resting conditions differ from the more focused singular response that occurs

during stress. The dynamics of this adaptive response have been referred to as “reactive tuning”

(2). In the field of nonequilibrium statistical mechanics, the relationship between the correlation

properties of the fluctuations of a system and its relaxation to equilibrium has be described by the

fluctuation-dissipation theorem (16). If the complex interactions of physiologic systems during

rest enable an organism to mount a focused adaptive response during a perturbation, the loss of

complexity in resting dynamics may indicate an impaired ability to adapt to stress and a

predisposition to functional decline.

MECHANISMS OF PHYSIOLOGIC COMPLEXITY

A variety of mechanisms probably underlie the complexity of physiologic systems,

including neuronal networks in the nervous system, biochemical pathways in metabolic control

systems, signaling pathways within and between cells, genetic switches, and transcription control

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elements. Two experiments highlight the importance of the autonomic nervous system in

generating the complexity of heart rate dynamics. When autonomic nervous system influences

on the heart are eliminated through the administration of the muscarinic receptor blocker

atropine and the beta-receptor blocker propranalol, the complex dynamics observed under

control conditions are lost (Figure 5).

In another study, baby pigs were shown to develop increasing heart rate complexity as

they matured from 8 to 33 days after birth (17) (Figure 6). During this period of time, the heart

becomes innervated by sympathetic nerves from the right stellate ganglion. When the right

stellate ganglion is denervated at birth, heart rate complexity does not develop. Thus, during

healthy development, complexity appears to emerge in physiologic systems such as heart rate,

and with senescence, system complexity is lost.

LOSS OF COMPLEXITY AS A PATHWAY TO FRAILTY IN OLD AGE

These considerations have led to the theory that the loss of complexity is the physiologic

basis of frailty in old age (2). This is illustrated in Figure 7. During youth, a multitude of

physiologic systems interact to produce a highly complex output signal (such as heart rate) that is

associated with a high level of physical function. With progressive aging, many of the

physiologic inputs and their connectivity are lost, resulting in a less complex output signal. This

loss of complexity is associated with a decline in functional ability. Finally, late in life,

physiologic inputs are diminished to the extent that the output becomes periodic or random, and

the individual crosses a frailty threshold. At this point they lose their ability to adapt to stress and

relatively minor perturbations such as new medications, a viral illness, or emotional trauma may

result in serious disability and death.

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INTERVENTIONS TO RESTORE COMPLEXITY IN PHYSIOLOGIC SYSTEMS

Fortunately, a number of novel interventions may be able to restore healthy dynamics in

elderly individuals and enhance their ability to adapt to a variety of external stimuli. Some

single interventions that have multi-system effects have already shown to improve functional

ability in older individuals. These include exercise (18), which can improve physical and mental

function, and medications such as beta-blockers, which reverse many of the physiologic

consequences of congestive heart failure. Other multifactorial interventions that address the

multiple systems that are impaired in individuals with syndromes such as falls (19) or delirium

(20) have also proven useful in clinical trials. Recently, Dr. Collins and colleagues have

demonstrated that low levels of mechanical or electrical noise can be used to enhance

somatosensation and thus improve postural control in healthy elderly subjects and patients with

diabetic neuropathy or stroke (21). New dynamic drug delivery systems provide more

physiologic drug administration and thereby enhance physiologic effects. For example, insulin

given in oscillatory fashion has a greater effect on glucose metabolism that when given

continuously (22). Similarly, when parathyroid hormone is give intermittently rather than

continuously, it increases bone mass in osteoporotic patients (23). Finally, external dynamic

control techniques such as pacing procedures to terminate cardiac arrhythmias have proven

useful in cardiac patients (24).

CONCLUSION

In conclusion, aging results in a number of changes in anatomic structures and

physiologic control processes that result in a reduction in system complexity and a loss of ability

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to adapt to common stresses in the external and internal environment. This loss of complexity

may be the physiologic basis of frailty. New interventions aimed at restoring complex dynamics

may be able to enhance physiologic adaptation and prevent the onset of disease and disability.

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Table 1: Decreased complexity of anatomic structures with aging.

Structure Measure Age Effect Neurons Dendritic arbor Loss of branches and neural

connections Bone Trabecular meshwork Trabecular loss and

disconnection Kidney Glomerular capillary tuft Degeneration and loss of

capillaries Subepidermis Elastic fibers and dermal

papillae Loss and collapse of subepidermal structure

Table 2: Decreased complexity of physiologic systems with aging.

System Measure Age Effect Heart rate dynamics 1/f slope, DFA, & approx.

entropy of interbeat intervals Decreased fractal scaling, more regular dynamics

Blood pressure dynamics 1/f slope, DFA, & approx. entropy of BP fluctuations

Decreased fractal scaling, more regular dynamics

Respiratory dynamics DFA of interbreath intervals

Loss of long range correlations in elderly males

Postural control 1/f slope of center-of-pressure trajectories

Decreased fractal scaling

Gait dynamics 1/f slope, DFA Decreased fractal scaling

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Table 3: Decreased Complexity in Disease

Disease

(ref) Measure

Alzheimer’s Disease (25)

EEG correlation dimension is reduced

Emphysema (26)

Reduced 1/f slope of size distribution of terminal airspace clusters

Ventric. Fibrillation (27)

Reduced HR fractal scaling (1/f slope*) and long-range correlations (DFA**)

Atrial Fibrillation (28)

Increased RR regularity (ApEn+) and decreased long-range correlations (DFA).

CHF and CAD (10, 29)

Reduced HR fractal scaling (1/f) and long-range correlations (DFA).

Aging and Hunting-ton’s Disease (15)

Loss of stride interval long-range correlations (DFA)

Breast Cancer (30)

Fractal Dimension of mammographic mass.

* 1/f = the slope of the log-transformed power spectrum (see text). **DFA = detrended

fluctuation analysis, a technique that quantifies the fractal-like correlation properties of time-

series data (see text).

+ ApEn = Approximate entropy, a measure of regularity in time series data (11). ApEn

quantifies the (logarithmic) likelihood that a series of data points that are a certain distance apart

for a given number of observations remain within the same distance on next incremental

comparisons.

Copyright (c) by The Gerontological Society of America. Reproduced from (2) by

permission of the Publisher.

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Table 4: Long-term Consequences of Complexity Loss

Study Authors/ref.

Subjects Complex System

Complex Measure

Adverse Outcome

Ho, et al. Circ.1997 (31)

52 CHF pts.+ 52 matched controls

RR interval (2o ECG)

DFA Mortality- 1.9 yrs.

Huikuri, et al. Circ.1998 (32)

347 random elders >65 yrs.

Heart rate (24oECG)

1/f slope Mortality- 10 yrs

Makikallio et al., AJC 1999) (27)

Case-control, post-MI +/- VF

RR interval (24oECG)

DFA 1/f slope

Ventricular Fibrillation

Huikuri, et al. Circ. 2000 (29)

446 MI pts w/ decreased LV fxn

RR interval (24oECG)

DFA Mortality- 1.9 yrs.

Makikallio, et al. AJC 2001 (33)

499 CHF pts. w/ EF< 35%

RR interval (24oECG)

DFA Mortality- 1.8 yrs.

Colantonio, et al. J. Geron. 1993 (34)

87 elderly stroke survivors

Psycho-social fxn.

Social net-work index

Fx’l loss, NH adm.

Fratiglioni, et al. Lancet 2000 (35)

Popn. of 1203 elders > 75 yrs.

Psycho-social Fxn.

Social network

Dementia

Copyright (c) by The Gerontological Society of America. Reproduced from (2) by permission of

the Publisher.

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Figure 1: Age-related decrements in physiologic performance. From Shock N, et. al.,

Baltimore Longitudinal Study on Aging (1).

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Figure 2: Continuous heart rate time series over 8 minutes for a healthy young subject (top

graph) and a healthy elderly subject (bottom graph). Note the similar average heart rate and

standard deviation of heart rate, but different dynamics as quantified by Approximate Entropy.

From (5) with permission from the American Medical Association.

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Normal Bone Osteoporotic Bone

Figure 3: Loss of Complexity in Bone

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0 10 20 30

-0.2

-0.1

0

0.1

0.2

0.3Young

time (s)

CO

P di

spla

cem

ent (

mm

)

0 10 20 30

-0.2

-0.1

0

0.1

0.2

0.3Elderly faller

time (s)

CO

P di

spla

cem

ent (

mm

)

0 0.5 1-4

-3.5

-3

-2.5

-2

-1.5

log 10 Frequency (Hz)

log

10Po

wer

(mm

2 /Hz)

Young

0 0.5 1-3.5

-3

-2.5

-2

-1.5

-1

-0.5

log 10 Frequency (Hz)

log

10Po

wer

(mm

2 /Hz)

Elderly faller

β = -1.21 β = -2.29

Figure 4: Center of pressure displacements (top graphs) and their corresponding log-transformed

power specta (bottom graphs) for a 30 year old healthy woman (left) and a 69 year old woman

with previous falls (right), obtained while the subjects stood on a force-plate for 30 seconds. The

slope of the regression line through the power spectra represents the scaling exponent β, which is

greater in the elderly faller than in the young subject, indicating a loss of complexity.

Copyright (c) by The Gerontological Society of America. Reproduced from (2) by permission of

the Publisher.

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Figure 5: The effect of autonomic blockade with atropine and propanolol on RR interval

dynamics in a healthy human subject.

SALINE

time, sec0 200 400 600 800 1000120014001600

RR

inte

rval

, sec

0.6

0.9

1.2

ATROPINE/PROPRANOLOL

time, sec0 200 400 600 800 1000120014001600

RR

inte

rval

, sec

0.6

0.9

1.2

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Figure 6: Interbeat interval (RR interval) time series over 200 seconds in 5 piglets as they

mature from 8 to 33 days of life. Note the increasing amplitude (standard deviation) and

irregularity (approximate entropy, ApEn) of the interbeat intervals with advancing postnatal age.

From (17) with permission of Elsevier Science.

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The Physiologic Basis of Frailty

Figure 7. The physiologic basis of frailty. Multiple interacting physiologic inputs (top) produce

highly irregular, complex dynamics (middle), that impart a high level of functionality (bottom)

on an organism. As the inputs and their connections degrade, the output signal becomes more

regular and less complex, resulting in functional decline. Ultimately, with continued loss of

physiologic complexity, function may fall to the critical level below which an organism can no

longer adapt to stress (the frailty threshold).

Copyright (c) by The Gerontological Society of America. Reproduced from (2) by permission of

the Publisher.

Inpu

ts

Out

put S

igna

l Fu

nctio

nal L

evel

Frailty Threshold

Age