19,
Gompertz in 1925 found that the age-specifie mortality rate in man as a
function of age increased exponentially over a considerable portion of life
and assumed that this phenomenon reflected an exponential decline with age of
some vital system.
In the field of radiation research Brues and Sacher [B1|
first introduced a mathematical approach to long-term mortality based on the
observation of Gompertz and this was followed later as a basis for the analysis of experimental data and for much theoretical formulations.
According to
this approach, the survival characteristics of a group of individuals may be
described by actuarial functions.
One of the most widely used is the Gompertz
function.
20.
The Gompertz function is the logarithm of the age-specific rate of
where
Q(t)
=
-
eB
Q(t)
z\a
mortality which is defined as
is the age-specific mortality and
surviving up to the time
t.
(1)
N
is the number of animals
Linearity of the Gompertz function with time
implies that
(t)
where
Py
and
P.
=
P_el
are positive constants.
(2)
Experience shows that a single acute
dose of radiation is followed (after a period of latency) by an upward displacement of the Gompertz function without change in slope, the amount of displacement
with respect to control being a function of dose.
tion would change the constant
Po
in equation (2), without affecting
single exposures would affect median survival,
t
where
a
(D)
In other words, acute irradia-
=
t
med’
linearly with dose
a- bD
is the median survival time of the control group and
dent constant.
P 1°
If
D, then
(3)
b
a dose-depen-
Chronic irradiation, on the other hand, characteristically in-
creases the slope of the Gompertz function proportionally to intensity of
irradiation, so that
med