Reliability-Engineering Approach

to the Problem of Biological Aging

Dr. Leonid A. Gavrilov, Ph.D.Dr. Natalia S. Gavrilova, Ph.D.

Center on Aging

NORC and The University of Chicago Chicago, Illinois, USA

What Is Reliability-Engineering Approach?

• Reliability-engineering approach is based on ideas, methods, and models of a general theory of systems failure known as reliability theory.

Reliability theory was historically developed to describe failure and aging of complex electronic (military) equipment, but the theory itself is a very general theory.

Why Do We Need Reliability-Engineering Approach?

• Because reliability theory provides a common scientific language (general framework) for scientists working in different areas of aging research.

• Reliability theory helps to overcome disruptive specialization and it allows researchers to understand each other.

Some Representative Publications on Reliability-Engineering

Approach to the Problem of Biological Aging

• Gavrilov, L.A., Gavrilova, N.S. The reliability theory of aging and longevity. Journal of Theoretical Biology. 2001, 213, 527-545.

• Gavrilov, L.A., Gavrilova, N.S. The quest for a general theory of aging and longevity. Science SAGE KE. 2003, 28, 1-10.

What are the Major Findings to be Explained?

1. Gompertz-Makeham law of mortality2. Compensation law of mortality3. Late-life mortality deceleration.

Biogerontological studies found a remarkable similarity in survival dynamics between humans and laboratory animals:

The Gompertz-Makeham Law

μ(x) = A + R0exp(α x)

A – Makeham term or background mortalityR0exp(α x) – age-dependent mortality

The Gompertz-Makeham law states that death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age.

Exponential Increase of Death Rate with Age in Fruit Flies

(Gompertz Law of Mortality) Linear dependence of

the logarithm of mortality force on the age of Drosophila.

Based on the life table for 2400 females of Drosophila melanogaster published by Hall (1969). Mortality force was calculated for 3-day age intervals.

Source: Gavrilov, Gavrilova,“The Biology of Life Span” 1991

Age-Trajectory of Mortality in Flour Beetles(Gompertz-Makeham Law of Mortality)

Dependence of the logarithm of mortality force (1) and logarithm of increment of mortality force (2) on the age of flour beetles (Tribolium confusum Duval).

Based on the life table for 400 female flour beetles published by Pearl and Miner (1941). Mortality force was calculated for 30-day age intervals.

Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

Age-Trajectory of Mortality in Italian Women(Gompertz-Makeham Law of Mortality)

Dependence of the logarithm of mortality force (1) and logarithm of increment of mortality force (2) on the age of Italian women.

Based on the official Italian period life table for 1964-1967. Mortality force was calculated for 1-year age intervals.

Source: Gavrilov, Gavrilova,“The Biology of Life Span”

1991

The Compensation Law of Mortality

The Compensation law of mortality (late-life mortality convergence) states that the relative differences in death rates between different populations of the same biological species are decreasing with age, because the higher initial death rates are compensated by lower pace of their increase with age

Compensation Law of MortalityConvergence of Mortality Rates with Age

1 – India, 1941-1950, males 2 – Turkey, 1950-1951, males3 – Kenya, 1969, males 4 - Northern Ireland, 1950-1952,

males5 - England and Wales, 1930-

1932, females 6 - Austria, 1959-1961, females 7 - Norway, 1956-1960, females

Source: Gavrilov, Gavrilova,“The Biology of Life Span” 1991

Mortality Kinetics for Progeny Born to Long-Lived (80+) vs Short-Lived Parents

Data are adjusted for historical changes in lifespan

Sons Daughters

Age40 50 60 70 80 90 100

Log(

Haz

ard

Rat

e)

0.001

0.01

0.1

1

short-lived parentslong-lived parents

Linear Regression Line

Age40 50 60 70 80 90 100

Log(

Haz

ard

Rat

e)

0.001

0.01

0.1

1

short-lived parentslong-lived parents

Linear Regression Line

Compensation Law of Mortality in Laboratory Drosophila

1 – drosophila of the Old Falmouth, New Falmouth, Sepia and Eagle Point strains (1,000 virgin females)

2 – drosophila of the Canton-S strain (1,200 males)

3 – drosophila of the Canton-S strain (1,200 females)

4 - drosophila of the Canton-S strain (2,400 virgin females)

Mortality force was calculated for 6-day age intervals.

Source: Gavrilov, Gavrilova,“The Biology of Life Span” 1991

The Late-Life Mortality Deceleration (Mortality Leveling-off, Mortality Plateaus)

• The late-life mortality deceleration law states that death rates stop to increase exponentially at advanced ages and level-off to the late-life mortality plateau.

• An immediate consequence from this observation is that there is no fixed upper limit to human longevity - there is no special fixed number, which separates possible and impossible values of lifespan.

• This conclusion is important, because it challenges the common belief in existence of a fixed maximal human life span.

Mortality at Advanced Ages

Source: Gavrilov L.A., Gavrilova N.S. The Biology of Life Span: A Quantitative Approach, NY: Harwood Academic Publisher, 1991

M. Greenwood, J. O. Irwin. BIOSTATISTICS OF SENILITY

Survival Patterns After Age 90 Percent surviving (in log scale) is

plotted as a function of age of Swedish women for calendar years 1900, 1980, and 1999 (cross-sectional data). Note that after age 100, the logarithm of survival fraction is decreasing without much further acceleration (aging) in almost a linear fashion. Also note an increasing pace of survival improvement in history: it took less than 20 years (from year 1980 to year 1999) to repeat essentially the same survival improvement that initially took 80 years (from year 1900 to year 1980).

Source: cross-sectional (period) life tables at the Berkeley Mortality Database (BMD):

http://www.demog.berkeley.edu/~bmd/

Non-Gompertzian Mortality Kinetics of Four Invertebrate Species

Non-Gompertzian mortality kinetics of four invertebrate species: nematodes, Campanularia flexuosa, rotifers and shrimp.

Source: A. Economos. A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 1979, 2: 74-76.

Non-Gompertzian Mortality Kinetics of Three Rodent Species

Non-Gompertzian mortality kinetics of three rodent species: guinea pigs, rats and mice.

Source: A. Economos. A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 1979, 2: 74-76.

Mortality Leveling-Off in Drosophila

Non-Gompertzian mortality kinetics of Drosophila melanogaster

Source: Curtsinger et al., Science, 1992.

Non-Gompertzian Mortality Kinetics of Three Industrial Materials

Non-Gompertzian mortality kinetics of three industrial materials: steel, industrial relays and motor heat insulators.

Source: A. Economos. A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 1979, 2: 74-76.

Aging is a Very General Phenomenon!

What Should the Aging Theory Explain:

• Why do most biological species deteriorate with age?

• Specifically, why do mortality rates increase exponentially with age in many adult species (Gompertz law)?

• Why does the age-related increase in mortality rates vanish at older ages (mortality deceleration)?

• How do we explain the so-called compensation law of mortality (Gavrilov & Gavrilova, 1991)?

Redundancy Creates Both Damage Tolerance and Damage Accumulation (Aging)

No redundancy

Dam age

Death

Dam age

RedundancyDam age accumulation

(aging)

Defect

Defect

Explanations of Aging Phenomena Using Reliability Theory:

1)(),,(nkxexXPxknF

Consequently, the failure rate of a system (n,k,x), can be written as follows:

nknxn-1 when x << 1/k (early-life period approximation, when 1-e-kx kx); k when x >> 1/k (late-life period approximation, when 1-e-kx 1)

nkx

nkxkx

eenke

dxxknSxkndSxkn

111

),,(),,(),,(

1

Consider a system built of non-aging elements with a constant failure rate k. If these n elements are mutually substitutable, so that the failure of a system occurs only when all the elements fail (parallel construction in the reliability theory context), the cumulative distribution function for system failure, F(n,k,x), depends on age x in the following way:

Therefore, the reliability function of a system, S(n,k,x), can be represented as:

11),,(1),,(nkxexknFxknS

Why Organisms May Be Different From Machines?

Way of system creationMachines: Assembly by macroscopicagents (humans)

Organisms: Self-assembly frommolecules and cells

R estric tions to the size of com pon entsM achin es: T en den cy tom acroscopic ity

O rganism s: T en den cy to m icroscopic ity(D N A , protein s, cells)

Degree of element miniaturisationMachines: Relatively low

Organisms: Extremely high

L im ita tion s to th eto ta l n u m b er o felem en ts in a sy stemM a c h in e s : V e r y s t r ic t lim ita tio n s

O rg a n ism s: L im ita t io n sa r e n o t s tr ic t

Demand for high initial quality of each element

Machines: Very high

Organisms: Relatively low

Expected systemredundancy

Machines: Relatively low

Organisms: Very high

Demand for high redundancy to be operational

Machines: Relatively low

Organisms: Very high

Expected system "littering"with initial defects

Machines: Low

Organisms: High

Opportunities to pre-test components(external quality control)

Machines: Practically unlimited

Organisms: Practically impossible

Differences in reliability structure between (a) technical devices and (b) biological systems

Each block diagram represents a system with m serially connected blocks (each being critical for system survival, 5 blocks in these particular illustrative examples) built of n elements connected in parallel (each being sufficient for block being operational). Initially defective non-functional elements are indicated by crossing (x).

The reliability structure of technical devices (a) is characterized by relatively low redundancy in elements (because of cost and space limitations), each being initially operational because of strict quality control. Biological species, on the other hand, have a reliability structure (b) with huge redundancy in small, often non-functional elements (cells).

Statement of the HIDL hypothesis:(Idea of High Initial Damage Load )

"Adult organisms already have an exceptionally high load of initial damage, which is comparable with the amount of subsequent aging-related deterioration, accumulated during the rest of the entire adult life."Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

Why should we expect high initial damage load ?

• General argument:--  In contrast to technical devices, which are built from pre-tested high-quality components, biological systems are formed by self-assembly without helpful external quality control.

• Specific arguments: 1. Cell cycle checkpoints are disabled in early development

    (Handyside, Delhanty,1997. Trends Genet. 13, 270-275 )

2. extensive copy-errors in DNA, because most cell divisions   responsible for  DNA copy-errors occur in early-life   (loss of telomeres is also particularly high in early-life)

3. ischemia-reperfusion injury and asphyxia-reventilation injury   during traumatic process of 'normal' birth

Spontaneous mutant frequencies with age in heart and small intestine

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35Age (months)

Mut

ant f

requ

ency

(x10-5

)

Small IntestineHeart

Source: Presentation of Jan Vijg at the IABG Congress, Cambridge, 2003

Birth Process is a Potential Source of High Initial Damage

• During birth, the future child is deprived of oxygen by compression of the umbilical cord and suffers severe hypoxia and asphyxia. Then, just after birth, a newborn child is exposed to oxidative stress because of acute reoxygenation while starting to breathe. It is known that acute reoxygenation after hypoxia may produce extensive oxidative damage through the same mechanisms that produce ischemia-reperfusion injury and the related phenomenon, asphyxia-reventilation injury. Asphyxia is a common occurrence in the perinatal period, and asphyxial brain injury is the most common neurologic abnormality in the neonatal period that may manifest in neurologic disorders in later life.

Practical implications from the HIDL hypothesis:

"Even a small progress in optimizing the early-developmental processes can potentially result in a remarkable prevention of many diseases in later life, postponement of aging-related morbidity and mortality, and significant extension of healthy lifespan."

"Thus, the idea of early-life programming of aging and longevity may have important practical implications for developing early-life interventions promoting health and longevity."

Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

Season of Birth and Female Lifespan8,284 females from European aristocratic families

born in 1800-1880Seasonal Differences in Adult Lifespan at Age 30

• Life expectancy of adult women (30+) as a function of month of birth (expressed as a difference from the reference level for those born in February).

• The data are point estimates (with standard errors) of the differential intercept coefficients adjusted for other explanatory variables using multivariate regression with categorized nominal variables.

Month of BirthFEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB.

Life

span

Diff

eren

ce (y

r)

1

2

0

3

p=0.02

p=0.006

Mortality Kinetics in Highly Redundant Systems

Saturated with Defects

) exp( )( )!1(

)( )(1

1

xRxeRikxmcekx x

n

i

i

s

Failure rate of a system is described by the formula:

where n is a number of mutually substitutable elements (connected in parallel) organized in m blocks connected in series; k - constant failure rate of the elements; i - is a number of initially functional elements in a block; λ - is a Poisson constant (mean number of initially functional elements in a block). Source: Gavrilov L.A., Gavrilova N.S. The reliability theory of aging and longevity. Journal of Theoretical Biology, 2001, 213(4): 527-545.

Dependence of the logarithm of mortality force (failure rate) on age

for binomial law of mortality

Age20 30 40 50 60 70 80 90

log 10

(mor

talit

y fo

rce

x 10

3 )

0.0

0.5

1.0

1.5

2.0

b(x0 + x)n

x0 = 100 years

n = 10

b = 10-24 yr-11

Failure Kinetics in Mixtures of Systems with Different Redundancy Levels

Initial Period The dependence of

logarithm of mortality force (failure rate) as a function of age in mixtures of parallel redundant systems having Poisson distribution by initial numbers of functional elements (mean number of elements, = 1, 5, 10, 15, and 20.

Failure Kinetics in Mixtures of Systems with Different Redundancy Levels

“Big Picture” The dependence of

logarithm of mortality force (failure rate) as a function of age in mixtures of parallel redundant systems having Poisson distribution by initial numbers of functional elements (mean number of elements, = 1, 5, 10, 15, and 20.

Strategies of Life ExtensionBased on the Reliability Theory

Increasing redundancyIncreasing durability of components

Maintenance and repair Replacement and repair

Two Illustrative Examples of the Recent Longevity Revolution in

Industrialized Countries:

• France

• Japan

Historical Changes in Survival from Age 90 to 100 years. France

Calendar Year1900 1920 1940 1960 1980 2000

Perc

ent S

urvi

ving

from

Age

90

to 1

00

0

1

2

3

4

5

6

FemalesMales

Historical Changes in Survival from Age 90 to 100 years. Japan

Calendar Year1950 1960 1970 1980 1990 2000

Perc

ent

Surv

ivin

g fr

om A

ge 9

0 to

100

0

2

4

6

8

10

FemalesMales

Conclusions (I)• Redundancy is a key notion for understanding

aging and the systemic nature of aging in particular. Systems, which are redundant in numbers of irreplaceable elements, do deteriorate (i.e., age) over time, even if they are built of non-aging elements.

• An actuarial aging rate or expression of aging (measured as age differences in failure rates, including death rates) is higher for systems with higher redundancy levels.

Conclusions (II)• Redundancy exhaustion over the life course explains the

observed ‘compensation law of mortality’ (mortality convergence at later life) as well as the observed late-life mortality deceleration, leveling-off, and mortality plateaus.

• Living organisms seem to be formed with a high load of initial damage, and therefore their lifespans and aging patterns may be sensitive to early-life conditions that determine this initial damage load during early development. The idea of early-life programming of aging and longevity may have important practical implications for developing early-life interventions promoting health and longevity.

AcknowledgmentsThis study was made possible thanks to:

• generous support from the National Institute on Aging, and

• stimulating working environment at the Center on Aging, NORC/University of

Chicago

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