McKay, Donald. "Front matter" Multimedia Environmental Models ...

that the uptake efficiency E A from food in the gastrointestinal tract of a “clean” fish
can also be described by a two-film approach yielding
©2001 CRC Press LLC
1/E A = A WK OW + A O
where A W and A O are water and organic resistance terms similar in principle to t W
and t O, but are dimensionless. A O appears to have a magnitude of about 2, and A W
a magnitude of about 10 –7 , thus, for all but the most hydrophobic chemicals, E A is
about 50%. When K OW exceeds 10 7 , the efficiency drops off, because of a high water
phase resistance in the gut.
A major difficulty is encountered when describing the loss of chemical in feces
and urine. In principle, D values can be defined, but it is quite difficult and messy
to measure G and Z; therefore, neither are known. It is probable that the digestion
process, which removes both mass and lipid content to provide matter and energy
to the fish, reduces both G A and Z A so that D E for egestion is smaller than D A. The
simplest expedient is to postulate that it is reduced by a factor Q, thus we estimate
D E for loss by egestion as D A/Q or D AE/Q, i.e., D E or D EE. The resistances causing
E A for uptake are assumed to apply to loss by egestion. This assumption is probably
erroneous, but it is acceptable for most purposes, especially because there is presently
an insufficiency of data to justify different values for uptake and loss.
The steady-state solution to the differential equation for the entire fish becomes
f F = (D Vf W + D Af A)/(D V + D M + D A/Q)
For the fish inside the epithelium, D A is replaced by D AE.
Assuming that f A equals f W, it is clear that f F will approach f W only when the D V
term dominates in both the numerator and denominator. If K OW is large, e.g., 10 6 ,
the term D A will exceed D V (because Z A will greatly exceed Z W), and the uptake of
chemical in food becomes most important. The fish fugacity then tends toward Qf A
or Qf W, i.e., the fish achieves a biomagnification factor of Q. Q is thus a maximum
biomagnification factor as well as being a ratio of D values.
This biomagnification behavior was first clearly documented in terms of fugacity
by Connolly and Pedersen (1988), Q typically having a value of 3 to 5. Biomagnification
is not immediately obvious until the fugacities are examined instead of the
concentrations. At each step in the food chain, or at each trophic level, there is a
possibility of a fugacity multiple applying. It is thus apparent that fish fugacities
and concentrations are a reflection of a complex combination of kinetic and equilibrium
terms that can in principle be described by D values.
The detailed physiology of the factors controlling Q has been investigated in a
series of elegant experiments by Gobas and colleagues (1993, 1999). The fugacity
change in the gut contents as they journey through the gastrointestinal tract was
followed by head space analysis. These experiments showed convincingly that the
hydrolysis and absorption of lipids reduces the Z value, causing the fugacity to
increase as a result of loss of the lipid “solvent.” Additionally, the mass of food is
reduced, thus G also decreases. The net effect is a decrease in GZ by about a factor
Q of 4. It is noteworthy that Q for mammals and birds is much larger, e.g., 30, thus