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

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