Reliability Theory of Aging

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Reliability Theory of Aging

• Dr. Leonid A. Gavrilov, Ph.D.
• Center on Aging
• NORC and The University of Chicago
• Chicago, Illinois, USA

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What Is Reliability Theory?

• Reliability theory is a general theory of systems
  failure.
• Reliability theory is a body of ideas,
  mathematical models, and methods directed to
  predict, estimate, understand, and optimize the
  failure distribution of systems and their
  components.
• Reliability theory allows researchers to predict
  the age-related failure kinetics for a system of
  given architecture (reliability structure) and
  given reliability of its components.
• Reliability theory was historically developed to
  describe failure and aging of complex electronic
  (military) equipment, but the theory itself is a
  very general theory.

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Some Representative Publications on Reliability
Theory of Aging(Additional Reading)

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• The reliability theory of aging and longevity.
  Journal of Theoretical Biology. 2001, 213,
  527-545.
• The quest for a general theory of aging and
  longevity. Science SAGE KE (Science of Aging
  Knowledge Environment). 2003, 28, 1-10.
• Reliability-engineering approach to the problem
  of biological aging. Annals of the New York
  Academy of Sciences. 2004, vol. 1019.
• Things fall apart Engineerings reliability
  theory explains human aging. IEEE Spectrum. 2004
  (in press).

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Why Do We Need Reliability Theory?

• Because reliability theory provides a common
  scientific language (general framework) for
  scientists working in different areas of aging
  research and anti-aging interventions.
• Reliability theory helps to overcome disruptive
  specialization and it allows researchers to
  understand each other.

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Most important, Reliability Theory goes to the
heart of the Aging problem

• Aging, according to reliability theory, is what
  makes "old not as good as new", when the failure
  rates are increasing with age.
• Non-aging objects are perfectly legitimate in
  reliability theory -- these are those objects,
  which do not deteriorate with age, when "old is
  as good as new", and when the failure rates are
  not increasing with age.
• Thus, the attempts to stop aging are not against
  the laws of Nature -- this is not about stopping
  or reversing the physical time, but rather the
  efforts to keep "old as good as new" through
  proper maintenance, repair and parts replacement.
• Thus, anti-aging interventions are perfectly
  legitimate according to Reliability Theory.

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According to Reliability TheoryAging is NOT
just growing oldInsteadAging is a degradation
to failure becoming sick, frail and
dead

• 'Healthy aging' is an oxymoron like a healthy
  dying or a healthy disease
• More accurate terms instead of 'healthy aging'
  would be a delayed aging, postponed aging, slow
  aging, or negligible aging (senescence)

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According to Reliability Theory

• Onset of disease or disability is a perfect
  example of organism's failure
• When the risk of such failure outcomes increases
  with age -- this is an aging by definition

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Implications

• Diseases are an integral part (outcomes) of the
  aging process
• Aging without diseases is just as inconceivable
  as dying without death
• Not every disease is related to aging, but every
  progression of disease with age has relevance to
  aging Aging is a
  'maturation' of diseases with age
• Aging is the many-headed monster with many
  different types of failure (disease outcomes).
  Aging
  is, therefore, a summary term for many different
  processes.
• Anti-aging interventions, therefore, should not
  be discouraged by their partial success limited
  to specific outcomes. There should be a complex
  of many different anti-aging interventions.

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What are the Major Findings to be Explained?
Biogerontological studies found a remarkable
similarity in survival dynamics between humans
and laboratory animals

• Gompertz-Makeham law of mortality
• Compensation law of mortality
• Late-life mortality deceleration.

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The Gompertz-Makeham Law
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.

• µ(x) A R0exp(a x)
• A Makeham term or background mortality
• R0exp(a x) age-dependent mortality

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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

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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

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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

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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

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Compensation Law of MortalityConvergence of
Mortality Rates with Age

• 1 India, 1941-1950, males
• 2 Turkey, 1950-1951, males
• 3 Kenya, 1969, males
• 4 - Northern Ireland, 1950-1952, males
• 5 - 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

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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

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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 (biological limit
  to human longevity).

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Mortality at Advanced Ages

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

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M. Greenwood, J. O. Irwin. BIOSTATISTICS OF
SENILITY
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Mortality deceleration at advanced ages.

• Risk of death (in log scale) is plotted as a
  function of age. Note that after age 95, the
  observed risk of death (black line) deviates from
  the Gompertz law (grey line) leveling-off at
  extreme ages.
• Source Gavrilov, Gavrilova, Things fall apart
  Engineerings reliability theory explains human
  aging. IEEE Spectrum. 2004 (in press).

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Mortality Leveling-Off in Drosophila

• Non-Gompertzian mortality kinetics of
  Drosophila melanogaster
• Source Curtsinger et al., Science, 1992.

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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.

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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.

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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.

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Aging is a Very General Phenomenon!
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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)?

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Redundancy Creates Both Damage Tolerance and
Damage Accumulation (Aging)
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Explanations of Aging Phenomena Using
Reliability Theory
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
Consequently, the failure rate of a system
?(n,k,x), can be written as follows
? nknxn-1

when x ltlt 1/k
(early-life period approximation, when 1-e-kx ?
kx) ? k

when x gtgt 1/k
(late-life period approximation, when 1-e-kx ? 1)
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Source Gavrilov, Gavrilova, Science SAGE KE.
2003, 28, 1-10.
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Why Organisms May Be Different From Machines?
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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).
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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.
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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

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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.

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Spontaneous mutant frequencies with age in heart
and small intestine
Source Presentation of Jan Vijg at the IABG
Congress, Cambridge, 2003
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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.
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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.

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Mortality Kinetics in Highly Redundant Systems
Saturated with Defects
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 ?
- 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.
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Dependence of the logarithm of mortality force
(failure rate) on age for binomial law of
mortality
Source Gavrilov, Gavrilova, Journal of
Theoretical Biology. 2001, 213, 527-545.
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Failure Kinetics in Mixtures of Systems with
Different Redundancy LevelsInitial 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.

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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.

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Strategies of Life ExtensionBased on the
Reliability Theory
Increasing durability of components
Increasing redundancy
Maintenance and repair
Replacement and repair
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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.

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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.

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Acknowledgments

• This 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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