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114                                                        The Toxicology of Fishes


                                   10.0
                                  DERMAL PERMEABILITY CONSTANT (mm/hr)  6.0  k s = 0.015  P sw + 6.46

                                    8.0

                                                                              .
                                                                       2
                                                                      r  = 0.18

                                    4.0



                                                                              .
                                    2.0
                                                                       2
                                                                      r  = 0.86
                                     0                                k s = 0.045  P sw + 0.60
                                      0      10      20     30      40     50     60      70
                                             SKIN–WATER CHEMICAL PARTITION COEFFICIENT
                       FIGURE 3.27 Dermal permeability of three chlorinated ethanes in rainbow trout and channel catfish as a function of
                       skin–water chemical partitioning. Fitted permeability coefficients for rainbow trout are given as solid circles. Open circles
                       represent fitted coefficients for channel catfish. Equations were generated for each species by simple linear regression.
                       (Adapted from Nichols, J.W. et al., Fundam. Appl. Toxicol., 31, 229–242, 1996.)


                       from that of Lien et al. (1994) to reflect more detailed aspects of vascular organization. Specifically,
                       anatomical studies with fish suggest that, although a portion of venous blood draining the skin contributes
                       directly to the mixed venous return, most of this blood flows to the caudal vein and from there to the kidney.
                        Assuming that chemical transfer between blood and skin is flow limited, a mass balance on the skin
                       compartment may be written as:
                                                                   s (
                                            VdC dt = (     C P s) + k A C w − C P sw)           (3.104)
                                                     Q C a −
                                             s
                                                s
                                                             s
                                                                     s
                                                                            s
                                                      s
                       where P  and P  are skin–blood and skin–water equilibrium partition coefficients. The first term on the
                             s
                                  sw
                       right-hand side of this equation is identical to that given previously for a flow-limited tissue (Equation
                       3.86), and the second term describes chemical diffusion across a membrane separating skin tissue from
                       the external environment. In this formulation, k  is the permeability coefficient defined as in Equation
                                                            s
                       3.1 (DP /h), and A  is the total skin surface area.
                             mw
                                      s
                        The dermal submodel was evaluated by exposing large trout and channel catfish to a series of
                       chlorinated ethanes in a chambered exposure system (McKim et al., 1996). For these studies, only the
                       trunk region of the fish was exposed. Chemical uptake across the skin then resulted in the accumulation
                       of chemical in blood and tissues and elimination across the gills. By using compounds for which validated
                       inhalation models already existed, it was possible to fit a set of apparent skin permeability coefficients
                       (k ) (Nichols et al., 1996). Figure 3.27 shows fitted permeability constants for three chloroethanes in
                        s
                       both trout and channel catfish. Fitted permeability coefficients increased little if at all with increasing
                       chemical affinity for skin. Based on this observation, the authors speculated that diffusion through tissue
                       water limits dermal flux of moderately hydrophobic compounds.
                       Dietary Uptake
                       Chemical and physiological factors that control xenobiotic uptake from the diet were described earlier
                       in this chapter. The dietary route of exposure may be important within an aquaculture setting as a means
                       of dosing animals with antibiotics and other therapeutic agents. Oral bioavailability defined using AUC
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