March 26, 2003
Help Available--Phenomenological Models for Research on Aging Arnold Mitnitski and Kenneth Rockwood
Arnold Mitnitski is in the Departments of Medicine and Computer Science, and Kenneth Rockwood is in the Department of Medicine (Geriatric Medicine & Neurology), Dalhousie University, Halifax, Nova Scotia, Canada. E-mail:
[email protected] (A.M.);
[email protected] (K.R.) ------------
Document URL: http://sageke.sciencemag.org/cgi/content/full/sageke;2003/12/vp2 Key words: aging • fitness • frailty • integrative approach • macroscopic state variable • mathematical modeling
In "Help Wanted: Physiologists for Research on Aging", George Martin challenged the scientific community to find better means of tackling the aging of the whole organism. He wrote "Aging involves each and every organ system. Organ systems communicate with each other in order to maintain homeostasis. We need to understand how these diverse systems integrate their several languages (endocrine, paracrine, autocrine). In addition, we need to decipher how these communications change over the life course. Solving such enigmas requires complex systems research into issues such as nonlinear dynamic networks, information theory, chaos, and fractals (1)." He suggested that we meet this challenge through integrative physiology, and he outlined a detailed plan for how an aspiring scientist might do so, right down to a trip to the National Institute on Aging (NIA) to liberate some extramural funds. Although such initiatives would be most welcome, we would like to propose an additional means by which scientists can take into account the integrative response of the organism and its changes over time. Like physiologists, physicists are concerned with the mechanisms that underlie the phenomena under investigation, and they also need to understand these phenomena at the level of integrated systems. In physics, although much progress has been made using mechanistic approaches, a complementary line of inquiry exists that is commonly referred to as a phenomenological approach. This method consists of systematizing facts that cannot necessarily be explained by considering those facts in isolation. Rather, a range of facts needs to be accommodated within a mathematical model. Using the
reductionistic (mechanism-based) approach, ad hoc theories (inevitably, many more than one) commonly emerge to explain the observed phenomena mechanistically. For the field to advance, however, these explanations need to fit within an overall framework of understanding. Such a phenomenological approach requires mathematical models, not just verbal descriptions. But it can exist prior to (and shed light on) the discovery of basic mechanisms. Returning to an example from physics, phenomenological thermodynamics was developed long before statistical mechanics. Phenomenological thermodynamics was not based on molecular mechanisms; indeed, it came into being even before the existence of molecules was accepted by all physicists. It is based on empirical observations of macroscopic behavior and not on a fundamental understanding of why matter behaves the way it does, but it nonetheless provides a set of mathematical relationships with enormous utility and power. Today, phenomenological thermodynamics and statistical mechanics happily coexist. We argue that the sort of integrative view envisaged by Martin might also be developed (perhaps even more quickly) using a phenomenological, rather than a reductionistic, framework. This is the case largely because a phenomenological approach is better suited to complex nonlinear systems that comprise a number of elements that interact with a strong stochastic component. Note that a "phenomenological model," in this sense, is distinct from how the term is used in the social sciences, where it commonly refers to a subjective, lived experience (for example, being part of a given society). Our argument is not to deny the importance of revealing such mechanisms as might underlie aging. Rather, our view is that integrative theories also should be sought, that they should be mathematized, and that the standard for their evaluation is whether they are compatible with all available evidence. Without a mathematical model, claims can become mantras, with only selective evidence in support of the claim, such as "complexity increases with aging," or "complexity decreases with aging." When should such models be proposed? Should we wait until the mechanisms (for example, at a genetic level) are established? Even if the mechanisms are known, how might we understand how they are manifested at the level of the whole organism? Because a phenomenological approach has been successfully applied to complex physical and chemical systems, and more recently in fields such as demography (2), our intention is to extend this approach to aging. Thus, we propose that aging be considered as a complex phenomenon, both at the individual level (as a process of the accumulation of deficits) and at the population level, using demographic, biomedical, and social characteristics of individuals. To undertake phenomenological studies is to take an approach complementary to that outlined by Martin in his commentary. There he envisaged the not-inconsiderable undertaking of recruiting samples of thousands of people and selecting among them on the basis of important individual characteristics that might minimize extraneous variability. It is for this reason that we argue that a phenomenological theory can be developed more quickly. The sort of approach that we have in mind can take advantage of the enormous amount of information now stored in a wide variety of existing databases
(for example, demographic, epidemiological, clinical, etc.). A huge number of such databases have been collected for a variety of purposes, and many are now in the public domain. On the friendly visit to the NIA envisaged by Martin, a considerably smaller sum of money might be liberated to formally reevaluate what is already known. Perhaps as Canadians, outspent per capita by our U.S. counterparts by an order of magnitude, it is the sort of thing we can try to do. The issue of individual differences in the aging process is one of the most challenging from both a theoretical and a practical standpoint. This issue is usually addressed in genetic studies, and Martin suggested that such studies include physiological assessments of people beginning in middle age in order to uncover the genetic basis of "elite" aging. Another way of understanding individual differences in aging is to use large collections of biomedical and epidemiological data, integrated with demographic characteristics in a mathematical model. To do so, we started with databases that contain information on elderly Canadians (3, 4) and later extended the approach to include all age groups (5) (we are presently considering other populations). By analyzing such databases, we tried to understand individual differences, using a variety of health-related variables such as symptoms and signs of various diseases or their resulting disabilities, or related laboratory abnormalities, as well as socioeconomic factors. We referred to abnormalities in these variables jointly as "deficits." Using a phenomenological paradigm, we attempted to model aging globally as a process of the accumulation of deficits in individuals (4). Because the dimensionality of data is high (we used from dozens to hundreds of variables usually associated with aging), we sought to avoid the notorious "curse of dimensionality" (6). The curse refers to computational intractability; for example, the estimation of the parameters in multivariable nonlinear models. At one point, scientists believed that such dependencies could be deciphered by high-speed computers, but this has proved not to be the case. In a model with 100 variables, the potential number of dependencies is, in the simplest case, in the thousands. Therefore, in practice, scientists simply assume independence among variables in multivariable modeling (7). As an alternative to this assumption, we proposed the use of one variable, which was calculated as the average of the count of deficits for a given individual. This variable can be thought of as a global characteristic of how people age. In these terms, those who accumulate more deficits can be considered to be in worse shape (biologically "older") than those who have accumulated fewer problems. We sought to verify our hypothesis by analyzing mortality patterns in relation to this count of deficits, which we termed a "fitness/frailty" index. This simple index correlated very highly (r = 0.996) with the mortality rate over 5 years of follow-up (4). The fitness/frailty index is calculated for each individual and shows a great deal of spread across individuals at the same age, reflecting their heterogeneity. The averaged index, across all the individuals at the same age, can also represent fitness/frailty at a population level. The average increases with age, reflecting the fact that people (on average) tend to accumulate problems as they become older. In consequence, it might even be possible to compare the health of populations on the basis of the trajectories of the accumulation of deficits.
We should note that this index does not fit completely with the definition of frailty as a specific clinical syndrome [for example, see (8)] and in a sense is more general, capturing notions of dynamics (the changing of variables over time) and complexity (interactions between the changing variables) (9). At the population level, the score increases exponentially with age, and it increases faster in men than in women (Fig. 1). The parameters of its increase were found to be close to 3% per year. This increase is quite robust with respect to the variables that make up the index. Indeed, simulations with different random compositions of the variables have led to similar results not only qualitatively but also quantitatively. In other words, the estimates of the parameters that we obtained depended more on the number of variables that constitute our index than on the nature of the variables. We take this to mean that the index is measuring biological redundancy, again reflecting the fact that the variables are highly interdependent. Thus, to some point, the higher the number of variables sampled, the more robust the estimate of the redundancy. In our experience, the smallest number of variables that can give a robust estimate is 20, and we have not seen much improvement in the precision of the estimate when the number of variables exceeds 40, but these boundaries require more formal investigation.
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Fig. 1. Accumulation of the proportion of deficits (frailty trajectories) with chronological age for men and women. Observed data are the proportion of deficits averaged across the same age group. Age group is representing by the midpoint (for example, the group aged from 60 to 65 years is represented by the point at 62 years). Solid lines represent the fitting of curves according to the two-component model: f(t) = G + F exp(bt), where f is the frailty index, t is the age, and G, F, and b are gender-dependent parameters (6).
Another interesting property is that the mortality rate can be expressed as a power-law function (see below) of the fitness/frailty index (10) The exponent is gender-specific, reflecting the fact that women have a higher chance of survival than do men when they have the same value of the fitness/frailty index. Put another way, men with a particular disability survive less often than do women with the same disability. We also think it likely that the exponent is population-specific, which suggests that it might constitute a means of summarizing the average age of different populations. In this regard, consider Fig. 2, which shows the relationship between mortality and the fitness/frailty index by sex. Fig. 1 illustrates that, at all ages, women show a higher level of frailty than men. Fig. 2, however, shows that, at any level of fitness/frailty, women
also have a lower mortality rate, or force of mortality [force of mortality is a term used (mostly in demographics) as a synonym for "rate of mortality" (other synonyms are "hazard function" in statistics and "failure rate" in engineering]. Note that for both wome n and men, the relationship between the force of mortality and the fitness/frailty index is a power law (a straight line on a log-log plot). Power law relationships are of some interest in biology and indeed have been proposed as the "footprint of a universal mechanism" (11). They have some interesting properties, including so-called "scale invariance," or being "scale-free" (another synonym is that they are "self-similar"). As an example, consider the relationship between the size and weight of an object. If a substance of uniform density increases by a standard width, its weight will increase by the cube of that change, and it will increase by that cube regardless of whether weight is measured in kilograms or pounds. Another example are so-called "fractal objects," which show the same pattern regardless of the level at which they are being observed. We have demonstrated a power-law relationship between the frailty index and mortality in one sample (10), and it is an area of active investigation by our group. Although it has yet to be refined, it potentially provides an attractive program for the integration of information. We suspect that it will be complementary to the integration, at the level of individual physiological systems, proposed by Martin. It is also likely to be a direct extension of earlier discussions about self-similarity by the sorts of integrative physiologists called for in the Martin commentary (12-14). It is in this sense that help is now available. Through the use of a program of phenomenological modeling, we might be able to achieve a better understanding of aging, which is surely one of the most perplexing problems now facing humanity.
Fig. 2. The force of mortality as a function of the fitness/frailty index in a log-log plot, in men (triangles) and women (circles). Solid lines represent the least-squares regressions.
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March 26, 2003 ------------
Comment on Article
References
1. G. M. Martin, Help wanted: Physiologists for research on aging. Sci. SAGE KE 2002, vp2 (6 March 2002) http://sageke.sciencemag.org/cgi/content/full/sageke;2002/9/vp2. 2. S. P. Kapitza, The phenomenological theory of world population growth. Phys. Uzpekhi. 39, 57-71 (1996). 3. A. B. Mitnitski, J. E. Graham, A. J. Mogilner, K. Rockwood, Frailty, fitness and latelife mortality in relation to chronological and biological age. B.M.C. Geriatr. 2, 1 (2002).[CrossRef][Medline] 4. A. B. Mitnitski, A. J. Mogilner, K. Rockwood, Accumulation of deficits as a proxy measure of aging. Sci. World J. 1, 323-336 (2001). 5. A. B. Mitnitski, A. J. Mogilner, C. MacKnight, K. Rockwood, The accumulation of deficits with age and possible invariants of aging. Sci. World J. 2, 1816-1822 (2002). 6. R. Bellman, Adaptive Control Processes: A Guided Tour (Princeton Univ. Press, Princeton, NJ, 1961). 7. S. K. Kachigan, Multivariate Statistical Analysis: A Conceptual Introduction (Radius Press, New York, ed. 2, 1991). 8. L. P. Fried, C. M. Tangen, J. Walston, L. P. Fried, C. M. Tangen, J. Walston, A. B. Newman, C. Hirsch, J. Gottdiener, T. Seeman, R. Tracy, W. J. Kop, G. Burke, M. A. McBurnie, Frailty in older adults. J. Gerontol. A Biol. Sci. Med. Sci. 56, M146-M156 (2001). [Abstract/Free Full Text] 9. K. Rockwood, R. A. Fox, P. Stolee, D. Robertson, B. L. Beattie, Frailty in elderly people: an evolving concept. C.M.A.J. 150, 489-495 (1994). [Medline] 10. A. B. Mitnitski, A. J. Mogilner, C. MacKnight, K. Rockwood, The mortality rate as a function of accumulated deficits in a frailty index. Mech. Ageing Dev. 123, 1457-1460 (2002). [CrossRef][Medline] 11. T. Gisiger, Scale invariance in biology: coincidence or footprint of a universal mechanism? Biol. Rev. Camb. Philos. Soc. 76, 161-209 (2001).[CrossRef][Medline] 12. F. E. Yates, Fractal applications in biology: Scaling time in biochemical networks. Methods Enzymol. 210, 636-675 (1992). [Medline] 13. L. A. Lipsitz, A. L. Goldberger, Loss of "complexity" and aging: potential applications of fractals and chaos theory to senescence. JAMA 267, 1806-1809 (1992). [Abstract] 14. B. N. Kholodenko, Power-law approximation and similarity properties of the regulatory characteristics of metabolism. Biofizika 28, 674-681 (1983). [Medline] 15. A.M. is a mathematician and Assistant Professor of Medicine and Computer Science at Dalhousie University, Halifax, Canada. K.R. is Professor of Medicine (Geriatric Medicine & Neurology) also at Dalhousie. His work is supported by the Dalhousie Medical Research Foundation as a Kathryn Allen Weldon Professor of Alzheimer Research and by an Investigator award from the Canadian Institutes of Health Research. The authors are grateful to A. J. Mogilner for invaluable illuminating discussions. Citation: A. Mitnitski, K. Rockwood, Help Available--Phenomenological Models for Research on Aging. Sci. SAGE KE 2003, vp2 (26 March 2003) http://sageke.sciencemag.org/cgi/content/full/sageke;2003/12/vp2
