Of three proposed acute toxicity models, the uptake–depuration (UD) model, the time-integrated concentration (TIC) model, and the concentration–time (CT) model are derived and verified with acute toxicity data to estimate the internal residues of waterborne metals in fish as a function of a few constants and variables. The main factors are the exposure time, the external exposure concentration, the bioconcentration factor (BCF), and the depuration rate constant (k₂). The UD model is based on the concept of residue levels at the cell membrane well correlating with the whole-body concentrations, whereas the TIC and the CT models are based on the idea of irreversible inhibition of the enzyme acetylcholinesterase (AChE) governing the metal acute toxicity in that metals in the entire fish or in the aqueous phase can be described by the critical area under the time–concentration curve that is associated with a critical TIC of toxicant in the target tissue. A highly significant correlation (r²>0.9) was found between predictions and LC₅₀(t) data for both the TIC and the CT models, indicating successfully describe 4- to 18-d LC₅₀(t) data of arsenic (As), cobalt (Co), copper (Cu), and Co/Cu mixture in rainbow trout (Oncorhyuchus mykiss) and of Cu in fingerlings and subadults of silver sea bream (Sparus sarba). The time-dependent lethal internal concentration at the site of action that causes 50% mortality is also predicted for a given compound and species. It concludes that the TIC and the CT models can be applied to regulate the acute toxicity and to estimate incipient LC₅₀ values and internal residues of waterborne metals in fish.
