Distribution and Pharmacokinetics Models - Pesticide Biotransformation and Disposition - page 134

derived the following equation for the average plasma concentration during any inter-
val τ at steady state:

FD
V k

FD

C

∞ =

=

τ .

(42)

τ Cl

d e

The average plasma concentration during the first dose interval (from time 0 to τ) is:

k FD
V k

1 − exp( − k τ ) 1 − exp( − k τ )

a e a

C = × − . (43)

τ ( − k ) k k

d a e e a

Substituting Eqs. (42) and (43) into Eq. (39) and rearranging yields the concentra-
tion index:

1

R = . (44)

C

k k

a e

1 − exp( − k τ ) − exp( − k τ )

e a

k − k k − k

a e a e

For chemicals with k a  k e , which is the case for many of the organochlorine
pesticides, for instance Zatz (1972) ,

FD
V k

C ( 1 exp( k ) ),

= − − τ (45)

e

τ

d e

and:

1

= (46)

R

) .

C

−

1 exp( k τ

e

The accumulation ratio ( R A ) for multiple exposures at fixed time intervals was
defined by Wagner (1967) as the ratio of the average mass of chemical in the body dur-
ing any exposure interval at equilibrium, and the average mass of chemical absorbed
after a single exposure. The average mass of chemical absorbed after a single exposure is
simply FD, the percentage of dose absorbed. Use of the relationship between concentra-
tion, mass, and volume of distribution shown in Eq. (21) allows Eq. (42) to be rearranged
to solve for the average mass of chemical during an exposure interval at steady state:

FD
k

∞ =

e τ .

(47)

A

Substitution of Eq. (23) into Eq. (47) yields:

∞ = 1 44

. FDt

1 2 /

. (48)

A

τ