Revival: Biological Effects of Low Level Exposures to Chemical and Radiation (1992)

2 BIOLOGICAL EFFECTS OF LOW LEVEL EXPOSURES

zian.2 The latter term was created by George Sacher to honor Benjamin

Gompertz (1779-1865) for advancing a rate theory approach to mortality

data. The son of an Amsterdam diamond merchant, Gompertz was the first

actuarial scientist to report that age-specific mortality increased exponen­

tially in adult human populations.34 Subscribing to what is now known as

the “wear-and-tear” theory of aging, Gompertz likened human mortality to

the “exhaustions of the receiver of an air pump by strokes repeated at equal

intervals of time.”

In its most generalized form,5 the Gompertz function is:

where Gx = the Napierian logarithm of the hazard function (i.e.,

the Gompertz function/transformation or Gom-

pertzian)

G0 = the vulnerability parameter

0x = either a linear or curvilinear function

G0 is an index of the vigor of the genotype in its environment.5 6 Gauging

population inability to withstand endogenous and exogenous mediated

injury,5 it provides the initial condition from which the second law of ther­

modynamics can impel the population from more ordered to less ordered

states.7 8 The derivative of </>x specifies the rate at which this progressive

instability (and, consequently, mortality) is manifested both from internal

and external sources. Thus, G0 and <j> are each dependent on genotype and

environment, as well as their interaction.9 Not surprisingly, there is consid­

erable variability in both Gc and <j> across human populations.1012 In terms

of our discussion, senescence and aging refer to those processes, in the

context of a hospitable, stable environment, that directly impact on Gc and

0.

For inbred, eutherian, mammalian laboratory populations housed under

good laboratory conditions and kept free of preventable disease, the sim­

plest Gompertz function that frequently characterizes mortality experience

is the linear form:

where a is a first-order mortality rate constant. In fitting Equation 3 —or

any Gompertz function —to data, Gx is estimated by taking the Napierian

logarithm of the age-specific mortality rate. Age-specific mortality rate, Qx,

is conveniently calculated by substituting A for d in Equation l:

( 4 )

( 2 )

(3)