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Ling M-P, Liao C-M, Tsai J-W, Chen B-C. 2005. A PBTK/TD modeling-based approach can assess arsenic bioaccumulation in farmed tilapia (Oreochromis mossambicus) and human health risks. Integr Environ Assess Manag 1:40–54.

The Appendix A was printed incorrectly in the original printed version of this article. The corrected Appendix A is given in its entirety below. Allen Press regrets the error.

APPENDIX A

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  2. APPENDIX A

PBTK model

The following assumptions were made to develop the PBTK model: (1) there is a five-compartment pharmacokinetic model of blood-gill-muscle-alimentary canal-liver, representing actual anatomical units of tilapia; (2) it is assumed that the gill acts as a continuously stirred tank reactor or well-mixed compartment into and out of which water flows, with chemical and oxygen being transferred to the tilapia, based on diffusive mass transfer; (3) a flow rate qij ≥ 0 gives the blood flow from the j-th blood compartment to the i-th organ compartment for Ij with 1 ≤ i, jn, in that all transport occurs by blood flow; (4) there is complete equilibrium of chemicals between the blood phase and the tissue phase of each compartment, and it is assumed that there is an inert soluble chemical with blood-chemical partitioning/binding coefficient fi present in amounts of chemical partitioned to compartment tissue i; (5) there is local mass balance of chemical substance, in that for each compartment, the amount of chemical substance entering is equal to the amount leaving; and (6) there is local mass balance of blood flow, in that

  • equation image

for 1 ≤ i ≤ n.

For the compartment of gill that interacts with As in external water, an additional process has to be considered (Thomann et al. 1997). An increased surface sorption to the gill surface was necessary. The exchange of As between internal gill tissue and the blood was therefore set at a lower exchange than the exchange between the gill surface and the water.

It can be seen from Equation 1 that d{C(t)}/dt ={[K]{C(t)}+[X]{u(t)}; using our assumptions, we developed a linear PBTK model (Figure 2) governing the principle features of the bioaccumulation and transport of As in tilapia in five target organs of blood, muscle, gill, alimentary canal, and liver, in that {C(t)} = {C2(t) C2(t) C3(t) C4(t) C5(t)} (μg g-1), respectively, describes the As concentration in blood, muscle, gill, alimentary canal, and liver; {u(t)} = Cw is the As

  • equation image((A1))

concentration in ambient water (μ L-1), and the state matrix [K] can be written as and input constant matrix

  • equation image((A2))