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Kinetics of Human Aging

I. Rates of Senescence Between Ages 30 and 70 Years in Healthy People

^a Division of Geriatrics, Department of Medicine, University of California School of Medicine, Los Angeles
^b Division of Biology and Medicine, Brown University School of Medicine, Providence, Rhode Island

F. Eugene Yates, Department of Medicine, UCLA, Medical Monitoring Unit, Suite 330, 1950 Sawtelle Blvd., Los Angeles, CA 90025-7014 E-mail: gyates{at}ix.netcom.com.

Decision Editor: John A. Faulkner, PhD

	Abstract

Top Abstract Methods Results Discussion Appendix I References

 
A calculation of loss rates is reported for human structural and functional variables from a substantially larger data set than has been previously studied. Data were collected for healthy, nonsmoking human subjects of both sexes from a literature search of cross-sectional, longitudinal, and cross-sequential studies. The number of studies analyzed was 469, and the total number of subjects was 54,274. A linear model provided a fit of the data, for each variable, that was not significantly different from the best polynomial fit. Therefore, linear loss rates (as a percent decline per year from the reference value at age 30) were calculated for 445 variables from 13 organ systems, and additionally for 24 variables even more integrative, such as maximum oxygen consumption and exercise performance, that express effects of multiple contributing variables and systems. The frequency distribution of the 13 individual system linear loss rates (as percent loss per year) for a very healthy population has roughly a unimodal, right-skewed shape, with mean 0.65, median 0.5, and variance 0.32. (The actual underlying distribution could be a truncated Gaussian, an exponential, Poisson, gamma or some other). The linear estimates of loss rates were clustered between 0% and 2% per year for variables from most organ systems, with exceptions being the endocrine, thermoregulatory, and gastrointestinal systems, for which wider ranges (up to 3% per year) of loss rates were found. We suggest that this set of linear losses over time, observed in healthy individuals between ages (approximately) 30 to 70 years, exposes the underlying kinetics of human senescence, independent of effects of substantial disease.

DEATH "from old age," independent of specific accident or major illness, occurs as a result of a linear decline of organ reserve with age ^{(1) (2) (3) (4)}. Although functional impairment from disease does not always follow a linear progression ⁽⁵⁾, losses attributable to normal aging can be estimated by using a simple linear model. The rate of this decline (senescence) has been shown, for exercise-related performance variables, to be slower among active individuals than for sedentary subjects ⁽⁶⁾. An empirical examination of rates of senescence for a set of variables from each of 13 organ systems allows for characterization of the distributional form of the various loss rates because of senescence, and a more precise determination of the median rate. We display the population of observed functional and structural loss rates (senescence rates) as a frequency distribution based on the aforementioned empirical studies.

	Methods

Top Abstract Methods Results Discussion Appendix I References

 
We reviewed the literature and restricted our analysis to healthy, nonsmoking, human subjects of both sexes. Data were collected from cross-sectional, longitudinal, and cross-sequential studies. The ages of the included subjects ranged from 18 to 100 years, with most of the data clustered between subjects aged 30 to 70 years. With the use of a Boolean AND search, the following subject keyword terms and phrases were included: aging, physiology; healthy; human; and the structural or functional variable being examined (e.g., brain weight, insulin sensitivity, forced vital capacity, etc.).

The functioning human being is composed of a set of state variables, and the set can be described, as a first approximation, by its basis elements and linear combinations of these elements. An analysis of senescence as a set of linear loss rates can be done by studying rates of decline for each basis element. Here we consider the basis elements to be 13 structural and functional systems, and the linear combinations to be the interactions among these systems. The Appendix lists the systems searched, and the variables examined for each system. Highly integrative variables, for example, maximum oxygen consumption and exercise performance, that involve the functions of and communications among many different organ systems were also analyzed. (Note: a different appendix, not shown, lists the many references from which the data were collected; it is available on request from the journal editorial office.)

Longitudinal and cross-sequential data were scarce, but when available, they were fitted with a polynomial if there were enough intermediate points. (Linear and curvilinear fits of the same data were compared by calculating the R² correlation function for both fits, and the coefficients of the x² term and the x term of a polynomial fit. The linear term carried almost all of the weight in the polynomial fit, as discussed later.) Cross-sectional data with intermediate points were not very common, but when they were available we used a polynomial fit, and the linear term again was shown to carry the most weight. Many of the studies reported only two data points: pooled values for a young group and an old group. For two-point data, we accepted a two-point line as a first approximation.

We take 30 years to be the age at which the baseline value (100%) of a capacity occurs (development is finished, and senescence begins). Each set of data was fit to the line

where

1. x is the age rounded to the nearest year,
   
2. y_x is the functional capacity at age x (as a percent remaining of the initial value at age 30),
   
3. k_s is the senescence loss rate as a percent per year, and
   
4. y₀ is the value at age 30 = 100%.
   

When an age range was reported for a given age group, but the average age was not reported, we used the midrange age as the age variable for the age group. Not all studies exhibited a uniform linear loss across all ages: the rates of loss decelerated for some studies in which data for more than two age groups were plotted as a function of age. In these cases we nevertheless chose to impose a linear fit on the data. In other cases, in which there was very little loss of function initially and a greater loss of function after age 50 (e.g., loss of smell identification), we again chose to calculate the linear regressions, starting at age 30.

Some variables were shown to increase with age yet still imply loss. One example of this phenomenon is reaction time: as this variable increases with age, it means that one is becoming slower. In these cases a positive slope was calculated, but it was considered to represent a decline in functional capacity and was entered as a negative slope (i.e., as a loss of capacity).

In some endocrine variables there is an abrupt change over a brief span of time, such as the fall of estradiol levels after menopause. In these cases, the loss is not gradual, and not even approximately linear, but is greatly, abruptly accelerated. Therefore, we did not include data on follicle-stimulating hormone, luteinizing hormone, estradiol, or progesterone in women. However, the rates of decline of these levels in men were included.

Limitations of Our Linear Estimates of Loss Rates
In addition to the limitation arising from the difficulty in finding data sets with enough measurements between the young (approximately aged 30 years) and old (approximately aged 70 years) to validate the linearity of the declines in capacities over the whole 40-year interval (discussed later), we also made a primary implicit assumption. We assumed that there is a single, underlying senescence process that affects most or all structures and functions and imposes a specific rate of change (mainly losses) on each (though the imposed loss rate can differ for different items.) Not all gerontologists would agree with this assumption—some believe that senescence is a continuation of development, that is, one phase of a single birth-to-death process. Miller ⁽⁷⁾ has strongly refuted that view, and we agree with his arguments.

A different assumption about changes in structure or function asserts that there is a succession of states and state transitions allowing for multidirectional patterns of growth and decline over the entire life span ⁽⁸⁾. According to this view, the focus should be on dynamics of state transitions that are some function of durations in states. It denies that change is necessarily progressive and detrimental. Some of these so-called duration-based changes depend on time since birth; some depend on duration in current state; some depend on time since a significant event in the contextual environment of the person (i.e., show history dependence). We prefer our present scheme on the basis of the available data—wherever we found sufficient data, we found decrements, and these appeared to be proceeding at nearly constant rates.

	Results

Top Abstract Methods Results Discussion Appendix I References

 
13 Organ Systems
The absolute value of each calculated linear loss rate was rounded to two significant figures, and a frequency distribution of the rounded rates was drawn for each system studied, as shown in Fig. 1. Each point in a distribution comes from a study, not an individual. The distributions are approximately uniform, with the values clustered between 0% and 2% loss per year for most variables. The exceptions are the thermoregulatory system (range 0 to 3.4), reproductive–endocrine system (range 0 to 3.1), endocrine system (nonreproductive, range 0 to 2.9), and autonomic nervous system (range 0.3 to 2.6), which have wider ranges; and the gastrointestinal system (range 0 to 3.2), whose distribution is unimodal, right skewed, with most values ranging from 0% to 2% loss per year. Some systems had distributions with very tight ranges: renal system, range 0.1 to 0.9; central nervous system (CNS), range 0 to 1.0; integumentary system, range 0.2 to 1.0; and circulatory–hematopoietic system, range 0 to 1.1. The linear loss rates for variables of the category "chromosomal structure and function" (i.e., DNA repair capacity and telomere length) all fell between 0.2% and 0.6% loss per year.

View larger version (81K): [in this window] [in a new window]   Figure 1. Individual system linear loss rate distributions and distribution for integrative variables analyzed. Frequency distributions of linear loss rates for 13 organ systems are shown in order from widest to narrowest distributions. The linear loss rate frequency distribution for integrative variables is shown last. CNS = central nervous system. ( Fig. 1 continues on next page.)

[_studies (no. of subjects in study x

calculated linear loss rate for study)]/

total no. of subjects in study.

The values for the different variables started at a reference value of 100% at age 30. They usually declined linearly over time, but some did not change (e.g., the gastrointestinal variable, gastric emptying time; and the musculoskeletal variable muscle volume). Some had relatively high loss rates (e.g., a variation in the RR interval of an electrocardiogram during sympathetic nervous system blockade, an autonomic nervous system variable that declined at a rate of -1.4% loss per year).

The steeper slopes (3% per year) were calculated for the thermoregulatory and reproductive-endocrine systems. These systems had weighted average linear loss rates of 0.95% and 1.28% per year, respectively. Dehydroepiandrosterone (DHEA) levels dropped very steeply (3.4% per year), whereas other hormone levels (e.g., free testosterone) had slower rates of decline (0.30–1.4% per year). The analyzed thermoregulatory variables mainly consisted of measured responses to cold stress or heat stress. The linear loss rate here reflects the rate of change of a rate of change.

There were 182 studies found for gastrointestinal (GI) variables; there were fewer studies analyzed for other systems, approximately 20 to 40. The disproportionate number of GI variables caused us to suspect that the shape of the distribution of GI rates ( Fig. 1) may have dominated the shape of the overall distribution ( Fig. 2). However, after GI variables are excluded and variables are plotted for all other systems, the distribution maintains its skewed shape, which we have likened to a truncated Gaussian form.

View larger version (22K): [in this window] [in a new window]   Figure 2. Frequency distribution of linear loss rates among the variables examined for all of the systems. A given value for a loss rate represents a constant, negative slope in percentage per year. This overall distribution appears to have a unimodal, right-skewed shape. The number of studies is 469. The median, mean, and mode values for this distribution are 0.5, 0.64, and 0.2% per year, respectively. The standard deviation among these rates is 0.56% per year.

Integrative Variables
Although many of the variables studied in the organ systems analysis involved cooperation among two or more functioning organ systems (e.g., FEV₁ or forced expiratory volume in 1 second, involves musculoskeletal function and respiratory function), a separate analysis was devoted to those "integrative" variables that required the function and interaction of nearly all of the organ systems. As exemplar, we examined maximum oxygen consumption and running performance studies in healthy, athletically trained and active individuals. Longitudinal studies (with a 20-year interval between measures) of marathon runners were included ⁽⁹⁾. The distribution of linear loss rates calculated for integrative variables is shown in Fig. 1. Among the integrative variables studied, the number of studies was 24, the number of subjects was 2421, the weighted average of linear loss rates was 0.97% per year, and the median loss rate was 0.9% per year.

The frequency distribution of linear loss rates for 13 organ systems plus the integrative variable is described in Table 2 . The mean was slightly higher (0.66% loss per year vs. 0.64% loss per year calculated for the frequency distribution of loss rates of the 13 organ systems alone), and the mode, variance, and standard deviation remained essentially unchanged when integrative variables were added. The contribution of integrative variables to this distribution is shown in Fig. 1. The linear loss rates are dispersed between 0% and -1.5% per year, with a unimodal, right-skewed distribution.

Justification of the Choice of a Linear Model for the Kinetics
Of the 469 studies examined, 245 had two data points, young and old, with average ages and averaged measurements of a given variable provided, and 224 had three or more data points. By system, the number of studies with intermediate data points was four for the autonomic nervous system, 30 for the CNS, three for chromosomal structure and function, 22 for the circulatory–hematopoietic system, 11 for the nonreproductive endocrine system, 24 for the reproductive–endocrine system, 66 for the gastrointestinal system, 13 for the immune system, one for the integumentary system, 10 for the musculoskeletal system, nine for the renal system, nine for the respiratory system, three for the thermoregulatory system, and 19 for integrative variables.

We did encounter some cases of curvilinear loss. However, the linear term in most polynomial fits carried most of the weight. For example, in a cross-sectional study of muscle cross-sectional area (data reference 62 in the Appendix not shown here), the parabolic fit for data (excluding values for data collected for subjects younger than age 30) was y = 4700 - 33x + 0.090x², where x = age, and y = cross-sectional area in square millimeters. In other kinds of cases, values reached steady levels in subjects aged 30 years, and linear loss began a later decade, after a delay.

Among the studies with four or more data points (two or more intermediate points), 14 had parabolic fits where R² > .9. The majority of these studies had linear fits where R² was also > .9. The largest changes in R² from linear to parabolic fit were in the following variables: smell (data reference 97), where linear R² was .8 and parabolic R² was .96; delayed memory recall (data reference 42), where linear R² was .65 and parabolic R² was .92; and block span (data reference 42), where linear R² was .69 and parabolic R² was .98 (Appendix not shown).

	Discussion

Top Abstract Methods Results Discussion Appendix I References

 
The decline of many important physiological functions was first shown to be very nearly linear by Nathan Shock ^{(1) (2) (3) (10)}. Variables such as nerve conduction velocity, basal metabolic rate, cardiac output, kidney blood flow, and maximum breathing capacity were shown to each have a different constant slope. Shock used data only from healthy human subjects in order to exclude changes caused by disease. However, he did not exclude smokers. Therefore, the decline in physiological function caused by smoking is a contributing factor to his slopes: it may be the reason that maximum breathing capacity was shown to have the steepest slope in his analysis.

Strehler and Mildvan studied linear decline by plotting percent reserve capacity against age ⁽⁴⁾. Their representation showed different variables to have similar slopes with linear loss values ranging from 0.9% to 1.4% of maximal reserve per year. This range was made even tighter in a recent report by Walter Bortz ⁽⁶⁾ that presents a global senescence rate of 1/2% per year for exercise-related variables among the healthiest people. Bortz also cites many examples of non-exercise-related variables (division of human skin fibroblasts, DNA repair, cerebral metabolism, rate of nail growth, appendicular bone calcium, and irregularity of the pulse rate) that decline at or near a rate of 1/2% per year. These past reports of linear loss inspired our endeavor to examine the distributional form of linear loss rates, using a much larger database.

Emphasis on Ages 30 to 70 Years
We focused our analysis on subjects aged 30 to 70 years in order to lessen confusion with changes attributable to development (that are present in persons aged less than 30 years), and changes depending only on compositional alterations of the population (i.e., survivor biases, which occur as the frail in a heterogeneous population are removed over time).

Age–Period–Cohort Problem
Because we were working with different populations, different study designs, and different study methods, both period and cohort error were introduced into our analysis. However, we do not expect the nominal rate-of-loss estimate to be substantially different among different types of studies, because we were dealing with such coarse estimates of loss rates.

Data Inconsistencies
Rates of loss calculated for the variable maximum oxygen consumption, in a study that tested men over a short-term follow-up of 4 years ⁽¹¹⁾, were larger with the use of cross-sectional data (-1% per year) than with the use of longitudinal data (0% per year). Furthermore, in a comparison of results of different longitudinal studies, estimates of calculated loss rates seemed to grow as the time interval between data points became larger: In a longitudinal study of maximum oxygen consumption in which the follow-up was done 20 years after the baseline study, a loss rate of -1% per year was reported ⁽⁹⁾, compared with a rate of the 0% seen over the shorter, 4-year follow-up in the study cited above.

Shape of Linear Loss Rate Frequency Distribution
Loss rates for some normal aging effects presented elsewhere ⁽⁵⁾ have been claimed to reveal a Poisson distributional character. In our data summarized in Fig. 2, there is a unimodal, right-skewed distribution that could have multiple interpretations. For example, it could be part of a Gaussian distribution that has been truncated so that any loss rates less than 0% per year (i.e., gains) are not seen. When the mirror image of the portion of the curve with loss rate values of 0.3% per year or greater is plotted as a reflection onto the left side of the x axis, a virtual, more complete, symmetrical "Gaussian" distribution is synthesized, which we then fitted to a formal Gaussian model ( Fig. 3) for illustration, to invite a search for some variables that may go in the opposite direction of those with loss rates. Are there no structural or functional variables that get better with age (left side of the Gaussian model)? We found a few reports of positive health changes that occur with age with respect to the "mind–body connection" ⁽¹²⁾. Experience and wisdom are two examples of improvements that, although hard to quantify, are imagined to increase as age advances, as are (for some individuals) work satisfaction and life satisfaction, but all these are very difficult to define and to quantify kinetically. One study showed an increase in the quality of wound healing in older people, although the time required for healing was longer ⁽¹³⁾. In the end, we did not find any quantitative data on biochemical, physiological, or behavioral improvements with age that were sufficiently detailed to permit us to estimate a kinetic coefficient for rate of gain over the 40-year age interval (30–70) of interest here.

View larger version (10K): [in this window] [in a new window]   Figure 3. Extrapolated Gaussian frequency distribution. With the true loss rate values plotted for 0–3.4% per year (filled squares), a mirror image (using the reflected values from 0.3 to 3.4 for unimodality) was plotted. For the reflection to be accommodated the abscissa was extended leftward as far as -3.2% per year. We then fitted a formal Gaussian equation to the extrapolated, now symmetrical, distribution of linear rates of change with age, between -3.2% per year (extreme gain) and +3.4% per year (extreme loss). The synthesized Gaussian curve is shown as the open diamond, bell-shaped curve.

Among possible choices as a model to fit the collection of loss rate parameters ( Fig. 2) are a Poisson, an exponential, a gamma, or a truncated Gaussian distribution. Each implies different characteristics of the underlying events—for example, of the degrees of independence among the many variables we studied. Therefore it would be worthwhile to determine whether or not any one of the mathematical forms for a distribution could account for the variance in the data of Fig. 2 better than the others. We attempted fitting these various distributional models to our data and concluded that the data are not sufficient to allow us to choose among the models, or even to ensure that any one of them is correct—though all appeared to be at least statistically plausible. Specifically, the data can be fitted by an exponential distribution with R² = .60, a Poisson distribution with R² = .36, a gamma distribution with R² = .64, and a (truncated) normal distribution with R² = .65.

What Underlies the Slopes of Loss
Because senescence is observed in nature in many diverse forms, there are currently at least 300 different theories of aging ⁽¹⁶⁾. Sacher divided specialized theories of aging, which he termed "aspect theories," into discrete types: descriptive, phenomenological, material, instrumental, formal, and evolutionary ⁽¹⁷⁾.

Many of the instrumental theories of aging, such as the free radical, immunological, toxicological, and endocrinological theories, are consistent with the observed linear loss of functional capacity with aging. Each of these theories describes a process that is gradual and steady, and requires a maintenance mechanism to prevent the harm that may result from it.

Telomere shortening, the basis of one material theory of aging, occurs linearly over time ^{(18) (19)} and begins before birth, whereas in our model we propose that senescence begins around age 30 years. It may be that the instability of chromosomes reaches a critical point by age 30 in humans such that it begins to manifest itself at higher levels of organization.

The evolutionary theory of aging predicts a late onset, progressive decrease in age-specific fitness of an organism because of internal physiological deterioration ^{(20) (21)} not prevented by any beneficial consequences of natural selection in the historical past. This aspect fits with our linear model of senescent loss, in which there is a gradual, persistent decrease in percent capacity remaining at a given age. Further, according to the evolutionary theory, aging is genetically and evolutionarily distinct from fitness: there is not necessarily a close positive correlation between fitness and aging, and organisms can evolve varying rates of aging, at least in part independently of the evolution of their fitness ⁽²¹⁾. Therefore, there is no contradiction between this theory and our model of a senescent individual described by a population of weakly correlated systems each declining at its own characteristic rate.

We conclude that the data-based model presented here has comprehensive features that encompass some of the salient properties of human senescence, and that it provides a kinetic measure that may prove useful in evaluating interventions to enhance health and life span.

	Acknowledgments

 
This work was supported in part by a gift from the Active Living Institute, Palo Alto, CA, and from ALZA Corporation, Palo Alto, CA.

We express our appreciation to Dr. Walter M. Bortz II and to Steven M. Pincus for helpful comments on the manuscript.

Received January 31, 2000

Accepted November 30, 2000

	Appendix I

Top Abstract Methods Results Discussion Appendix I References

 

	References

Top Abstract Methods Results Discussion Appendix I References

 

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