Caos Fractales y Enf

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C h a o s , F r a c t a l s , a n dO u r C o n c e p t o f D i s e a s e

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ABSTRACT The classic anatomo-clinic paradigm based on clinical syndromes isfraught with problems. Nevertheless, for multiple reasons, clinicians are reluctant to em-

brace a more pathophysiological approach, even though this is the prevalent paradigmunder which basic sciences work. In recent decades, nonlinear dynamics (chaos the-ory) and fractal geometry have provided powerful new tools to analyze physiologicalsystems. However, these tools are embedded in the pathophysiological perspective and

are not easily translated to our classic syndromes.This article comments on the problemsraised by the conventional anatomo-clinic paradigm and reviews three areas in which

the influence of nonlinear dynamics and fractal geometry can be especially prominent:disease as a loss of complexity, the idea of homeostasis, and fractals in pathology.

THE CONCEPT OF DISEASE is deeply rooted in medical practice, and one canhardly conceive of caring for patients without this tool. Nevertheless, underthis seemingly uncontroversial idea there are some highly polemical axioms that

we usually take for granted, even though they often lead us to some uncom-

fortable inconsistencies and contradictions. Some of the conceptual issues de-

rived from our traditional view of disease, which condition the way we conceive

and practice medicine, include:

1. An ontological idea of disease. We conceive of disease as a real entity that af-fects a previously healthy person, thus making him ill.The purpose of medicine

*Department of Internal Medicine, Hospital de Mstoles, Spain.Department of Pathology, Hospital de Mstoles, Spain.Correspondence: Manuel Varela, Department of Internal Medicine, Hospital de Mstoles, c/Rio

Jucar s/n, Mstoles, Madr id 28935, Spain.E-mail: [email protected].

Perspectives in Biology and Medicine, volume 53, number 4 (autumn 2010):58495 2010 by The Johns Hopkins University Press

Manuel Varela,* Raul Ruiz-Esteban,* an d

M a r i a J o s e M e s t r e d e J u a n


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is to identify and fight this entity. If it succeeds, the patient is cured; otherwise,

the patient will remain sick (chronic disease) or will die. A key aspect of this

framework is the idea of lesion as the ultimate mechanism of disease. Neverthe-less, this scheme is continuously contradicted by our daily practice, in which we

have to deal with fading boundaries between health and disease (both in time

and in diagnostic criteria). One can of course argue that the idea of illness is just

a conceptual crutch, and that we dont really believe in diseases, but this para-

digm is extremely resilient, and one can hardly imagine how to practice medi-

cine without the concept of disease.

2.An overwhelming trend to dichotomize.This applies not only to the health/dis-

ease contradiction, but to almost every medical sign or symptom. Even obviously

continuous variables (temperature, blood pressure, glycemia) are immediately

dichotomized (febrile/afebrile), using an often arbitrarily drawn threshold, or

red line.This is not a particularity of clinical reasoning, and it probably reflectsa deeply rooted tendency in the human psyche (Rubia 2007). However, it is

especially evident (and often confusing) in medical practice.

3.A nave causal reasoning. Disease is usually considered the result of an aggres-

sion, often coming from outside (such as infectious diseases), that disrupts the

normal equilibrium (health) and makes the patient ill.The profound crisis that

has shaken many areas of natural sciences during the 20th century (quantum me-

chanics, chaos theory, systemic thinking) has hardly touched medicine, but even

within our classical mechanistic paradigm, we constantly face obvious insuffi-

ciencies and contradictions. For example, while it is generally accepted that the

cause of tuberculosis is Mycobacterium tuberculosis, we tend to overlook the fact

that less than 5% of subjects colonized by this germ finally develop the disease

(Bates and Stead 1993). Obviously, some other causes, such as immune status,

must play a role, and we have to recur to a statistical/probabilistic multicausal

model that, while scientifically sound and practical, is conceptually quite frus-

trating (Krieger 1994; Susser 1973).

4. Illness conceived as a loss of order.We tend to consider health as a state of equi-

librium and smooth regularity, and disease as a perturbation of this natural

order. In several languages the word disorder is also a synonym for disease.Again,

this is probably just a prejudice. Living systems are characteristically far away

from thermodynamic equilibrium; most healthy behaviors are highly irregular

and pseudo-random; and the loss of this pseudo-randomness (the emergence ofrhythms) is a hallmark of disease. In fact, rhythms are used as essential keys in the

diagnosis of many diseases (tremor in Parkinsons disease, seizures in epilepsy,

Cheyne- Stockes respiration in certain neurologic disorders, mood swings in

bipolar disorders).

5.The concept of homeostasis.We assume that organisms have some kind of con-

trol systems responsible for keeping physiologic variables within certain limits.A

departure from normality would unleash specific correcting mechanisms aim-

ing to revert the system to its basal status. Again, this is probably a wild over-

C h a os, F ra ct al s , a n d O u r C on cep t of D is eas e

autumn 2010 volume 53, number 4585


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simplification, and there are no such simple cybernetic systems (Romanovsky

2007).

In this conventional concept of disease one can easily perceive the echoes ofthe old prescientific idea of possession: something that pushes the subject away

from natural order and requires that nature act to restore health. If this is not

enough, we physicians will try to exorcise the ailment. All the metaphoric dis-

course of medicine is full of this idea of fight against evil (and we have a thera-

peutic armamentarium, an antibiotic strategy, or a concept of the immune sys-

tem as a home police).

However, this is not the only existing paradigm. Since the 19th century, there

has been a strong pathophysiologic school, hegemonic in basic sciences, that

maintains important differences with the classic anatomo-clinical conception.

Patho-physiologists understand disease as a quantitative change in the same

processes that operate in the healthy subject and assume the lesion is the conse-quence, rather than the cause, of the pathologic phenomenon.Therefore, instead

of searching for specific lesions and naming clinical syndromes, medicine should

focus on measuring these pathophysiological processes and interpreting them as

variations of the same usual physiologic systems operating in every subject.This

is the prevailing paradigm in basic sciences, where most of the major innovations

are developed. However, clinicians (and patients) feel uncomfortable in this ever-

flowing scenario, and it is not clear how most of our conceptual tools (includ-

ing evidence-based medicine) can be transported to this new setting.Therefore,

in this struggle between anatomo-clinic and pathophysiological approaches,

most clinicians will take sides with the classic anatomo-clinic conception. Con-

sequently, we have to painstakingly translate most of the scientific production

(developed under the pathophysiological paradigm) to our old-fashioned clini-

cal syndromes. Arguably, this increasingly difficult translation may be a cause of

the widening gap between basic research and clinicians (Lenfant 2003).

Recently, new disciplines such as nonlinear dynamics (chaos theory) and

fractal geometry have brought new tools and perspectives into pathophysiology

and may shed new light on these issues. Many physiological systems are highly

complex networks, with many recursive feed-back and feed-forward circuits, and

thus they may be especially prone to develop chaotic behaviors and display frac-

tal structures. Therefore, nonlinear dynamics and fractal models have been in-

creasingly applied in physiology and medicine. Table 1 offers an obviously notexhaustive list of examples.

Although belonging to different settings (fractals are spatial structures, while

chaotic dynamics refer to time series), fractals and chaotic systems have profound

relations. Most notably, one of the main characteristics of both is the presence of

power law distributions (scaling). In fractal structures, the perimeter and the size

of the measuring unit follow a power law (perimeter ~ length unit a), where a

is related to the fractal dimension.A similar power law is characteristic of chaotic

dynamics (for example, period distribution), where a is related to the complex-

586

M . V ar e l a , R . R u i z -E s t e b an , a n d M . J . M e s t re d e J u a n

Perspectives in Biology and Medicine


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ity of the dynamical system. Furthermore, natural fractals are usually the conse-

quence of chaotic systems (orography and weather, coastlines and waves, cloudsand winds), while the strange attractors that characterize chaotic systems typi-

cally have a fractal structure.That is why it is sometimes said that chaos and frac-

tals represent similar behaviors, chaos belonging to the temporal dimension,

while fractals take place in space.

Chaos and fractal geometry are important not only because of their wide-

spread utilization, but also because they are in some ways radically subversive and

erode some deeply grounded convictions.At times they only seem to pose some

mathematical paradoxes (for example, fractal bodies have a finite area but an infi-



Table 1 AR E A S I N W H I C H N O N L IN E A R D YN A M I CS A N D F R AC T AL G E O M E TRY

H AV E B E E N A P P L I E D

aging Goldberger et al. 2002; Huikuri et al. 1998; Iyengar et al. 1996; Lipsitz and

Goldberger 1992; Pikkujamsa et al. 1999

arrhythmia Bigger et al. 1996; Lombardi 2000; Makikallio et al. 1997; Vikman et al. 1999

blood pressure Marsh, Osborn, and Cowley 1990

breathing Dirksen et al. 1998; Frey et al. 1998; Suki 2002; Szeto et al. 1992

dementia Abasolo et al. 2006; Jeong 2004

diabetes Churruca et al. 2008; Ogata et al. 2006, 2007

endocrinology Pincus 2001; Pincus et al. 1999

epilepsy Lehnertz 1999

fetal distress Li et al. 2005

genetics Havlin et al. 1995; Peng et al. 1992

heart failure Goldberger 1997; Ivanov et al. 1999; Makikallio et al. 1997, 1999; Peng et al.1995;Vikman et al. 1999

heart rate Goldberger, Rigney, and West 1990; Goldberger et al. 2002

ischemic heart disease Bigger et al. 1996; Makikallio et al. 1999

multiple organ failure Lundelin et al. 2010; Papaioannou et al. 2006; Seely and Christou 2000;Tibby

et al. 2003;Toweill et al. 2000;Varela et al. 2005, 2006

neurodegenerative Aziz and Arif 2006; Hausdorff et al. 1997

syndromes

neurology Lefevre 1983; Kitaoka,Takaki, and Suki 1999; Mietus et al. 2000; Mutch et al.

2000;Weibel and Gomez 1962

pathology Boxt et al. 1994; Cross and Cotton 1994; Dioguardi et al. 2003, 2006; Gaudio

et al. 2005; Huang and Lee 2009; Lorthois and Cassot 2010; Losa and

Nonnenmacher 1996; McNamee 1991;Tambasco 2008postural control, gait Hausdorff et al. 1995, 1997; Peterka 2000; Riley et al. 1997

radiology Caldwell et al. 1990; Kuklinski et al. 1989; Mitsunobu et al. 2003; Nelson

1990

speech disorders Jiang, Zhang, and McGilligan 2006; Rahn et al. 2007;Voss and Clarke 1975;

Zhang et al. 2005

stroke Hornero et al. 2005, 2006

temperature Varela, Jimenez, and Farina 2003


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nite perimeter), but what they really mean is equivalent to what quantum

mechanics meant for classic physics: the end of certainty. Conventionally, we tend

to believe that imprecision, ambiguity, or uncertainty are only the consequencesof insufficiencies of our models or of our techniques, and that by improving our

instruments we can endlessly improve our predictions. However, this is not true

in chaos. Uncertaintynot randomnessis inherent to these systems, and we

have to cope with the fact that our predictive power is limited, no matter the

instruments we use. Another deeply unsettling property of chaos is emergence:

the capacity of these systems to collapse chaos and develop a highly ordered be-

havior that appears out of the blue and that, again, we are not able to predict

a priori.

Obviously these are still young disciplines, and only time will show the real

influence of chaos and fractal geometry in medicine. But for their rather short

life with us, they have certainly made a racket.There are at least three aspects inwhich these disciplines have been especially influential.

D i s e a s e a s a L o s s o f C o m p l e x i t y

The conventional idea that health implies order and predictability, whereas dis-

ease is characterized by a disordered output, is constantly being contradicted by

facts. Many physiological systems are highly irregular and unpredictable (pseudo-

random), and the loss of this irregularity is one of the earliest signs of dysfunc-

tion. This should not be so counterintuitive: it is hardly surprising that a com-

plex physiological system, when injured (for example, by losing afference or

processing power) would display a poorer, less complex output.There may be also a semantic problem: the idea of complexity, although quite

intuitive, is not easy to formalize, and it is only recently that algorithms have

been developed to measure it.These tools have not yet been widely introduced

in daily practice, but there is increasing evidence for the relationship between

loss of complexity and aging or disease.The field where this has been most ex-

tensively studied is heart rate variability, where it has been shown to have impor-

tant prognostic implications in several areas, including heart failure, arrhythmic

death, forecasting the development of atrial fibrillation, and predicting mortality

in the elderly (Bigger et al. 1996; Huikuri et al. 1998; Makikallio et al. 1999;Vik-

man et al. 1999). Several other central physiologic systems display similar behav-

iors. In thermoregulation, a loss of complexity of the temperature curve is asso-

ciated with increased mortality in critically ill patients, independently of the

presence of fever (Varela et al. 2005, 2006). Glycemic profile is significantly less

complex in diabetic patients than in healthy volunteers, and probably this find-

ing precedes the development of full blown diabetes in patients with the meta-

bolic syndrome (Churruca et al. 2008; Ogata et al. 2006). In critically ill patients,

complexity of the glycemic profile is inversely correlated with mortality, inde-

pendently of the presence of diabetes (Lundelin et al. 2010). Similar findings

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have been published for Alzheimers dementia, fetal distress, aging, epilepsy, and

the genetic code, among others (Abasolo et al. 2006; Havlin et al. 1995; Jeong

2004; Lehnertz 1999; Li et al. 2005; Lipsitz and Goldberger 1992).

Homeostasis Revised

Homeostasis has been a key idea in physiology since the 19th century.Thermo-

regulation is a classic example. Conventional wisdom assumes the existence of a

hypothalamic thermostat that compares the actual body temperature with a

preestablished setpoint, and consequently triggers the corresponding heat-con-

serving or heat-dissipating reactions. However, this is at best a gross oversimpli-

fication (Romanovsky 2007), and the emerging picture is that of a network of

interconnected but independent circuits, each one reacting to different temper-

ature ranges in distinct ways.The final portrait is quite different to the classicalcybernetic thermostat, but it could be a typical example of a nonlinear dy-

namic system. This characteristic is not unique to thermoregulation: it can be

found in several other physiological systems having multiple overlapping and

redundant feed-forward and feedback loops, and producing a highly complex,

pseudo-random output.

There are several striking similarities between these systems and the strange

attractors emerging in nonlinear dynamic models.1 First, they tend to develop

spontaneous quasi-rhythmic behaviors (circadian rhythm, heart rate, breathing).

Second, they are very robust: they are able to keep their output within certain

boundaries even faced with extreme inputs (thermoregulation, glycoregulation).

And third, they are effective in escaping reverberant or resonant behaviors. Fur-thermore,avoiding strict patterns helps in distributing stress and retarding failures.

This nonlinear dynamic model does not dismantle the homeostasis paradigm,

but it obviously changes it radically. In addition, it provides some very useful

tools and metrics that, although not yet widely introduced in general practice,

may change our way of understanding and dealing with disease.

Fractal s in Phys iol ogy and Medicine

Fractals are characterized by being scale-freein other words, they appear very

similar whatever the scale used to look at them (Figure 1). Obviously, natural

fractals can only maintain this characteristic within certain size boundaries, butthere are a surprising number of fractal-like structures in normal anatomy (bron-



1An attractor is a set to which a dynamical system evolves after a long enough time.That is, points

that get close enough to the attractor remain close even if slightly disturbed. Geometrically, an

attractor can be a point, a curve, a manifold, or even a complicated set with a fractal structure

known as a strange attractor. Describing the attractors of chaotic dynamical systems has been one of

the achievements of chaos theory (http://en.wikipedia.org/wiki/Strange_attractor#Strange_

attractor).


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chial tree, blood vessels, cardiac conduction system; see Figure 2).This remake of

similar patterns at different sizes is a consequence of the power law governing its

structure, and it is analogous to the scaling of frequencies that characterizes

chaos.

Fractal geometry has several obvious physiological advantages. First, it is a very

efficient topological converter.When a transporting system (three-dimensional

pipe tube) becomes an exchange or diffusing system (two-dimensional sur-

face), there is often a fractal structure in between. In addition, it can be devel-

oped by means of an extremely simple algorithm. Further, its scaling properties

makes it adaptable to diverse space constraints. Finally, it is robust and can with-

stand severe injuries while maintaining its functionality.

Here again, pathology often appears as a loss of complexity (for example, pul-

monary emphysema, osteoporosis, diabetic retinopathy), and new tools derived

from fractal geometry may change our perception and our way of classifying dis-

590



Figure 1

Two examples of self-similarity. Left: Self-similarity in space: fractal structure. Each branch resemblesthe original at a smaller scale. Right: Self-similarity in time.A fractal process such as heart rate

displays fluctuations on different time scales that are statistically self-similar.

SOURCE: GOLDBERGER (1996), WITH PERMISSION.


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eases. Conventional anatomo-pathology operates in two distinct scenarios: a

three-dimensional macroscopic field (which describes brain infarcts or tubercu-

lous caverns), and a two-dimensional microscopic range (which describes con-

ditions like adenocarcinoma, glomerulonephritis). However, certain structures

are characterized by a delicately woven fractal structure, often involving several

systems (alveolar/capillary in the lung, hepatocytes/sinusoids/biliary ducts in the

liver). Classic pathology has no instrument (at least in everyday practice) to visu-

alize, let alone measure, these structures, and therefore we remain blind to the

unfolding from the two-dimensional microscopic to the three-dimensional

macroscopic levels.

Nonetheless, it is at this mid-range level that some of the most prevalent func-

tional pathologies operate. Portal hypertension, a cardinal characteristic of hepa-

tic cirrhosis, is in great measure the consequence of this kind of structural

derangement. One of the key problems in chronic obstructive lung disease is alve-

olo-capillary mismatch, and pathology can say nothing about it. Fractal geometry

may offer some tools to tackle these problems (Dioguardi et al. 2003, 2006;

Gaudio et al. 2005; Glenny, Bernard, and Robertson 2000).

In the anatomo-clinic versus pathophysiologic dilemma, nonlinear dynamics



Fractal structure: Cast of a human lung.

SOURCE: PROF. EWALD R. WEIBER, ANATOMIC INSTITUTE, BERN UNIVERSITY.

Figure 2


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and fractal geometry will not be neutral.Their emphasis in measuring quantita-

tive variables, present both in healthy subjects and in patients, will make ever

fuzzier the (hypothetical) line separating health from disease and thus will pro-vide powerful arguments and tools to the pathophysiologists side. On the other

hand, these disciplines are giving us some extremely useful diagnostic and prog-

nostic information, that, as clinicians, we cannot ignore, pushing us therefore

towards the pathophysiologic paradigm.

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