very common assumption. In that case the gut equation is augmented with an input term, with an absorption rate constant Ka: That requires defining an equation for the quantity ingested and present in the gut lumen: In the absence of a gut compartment, input can be made directly in the liver. However, in that case local metabolism in the gut may not be correctly described. The case of approximately continuous absorption (e.g. via drinking water) can be modeled by a zero-order absorption rate (here Ring in units of mass over time): More sophisticated gut absorption model can be used. In those models, additional compartments describe the various sections of the gut lumen and tissue. Intestinal pH, transit times and presence of active transporters can be taken into account . Skin depot The absorption of a chemical deposited on skin can also be modeled using first order terms. It is best in that case to separate the skin from the other tissues, to further differentiate exposed skin and non-exposed skin, and differentiate viable skin (dermis and epidermis) from the stratum corneum (the actual skin upper layer exposed). This is the approach taken in [Bois F., Diaz Ochoa J.G. Gajewska M., Kovarich S., Mauch K., Paini A., Péry A., Sala Benito J.V., Teng S., Worth A., in press, Multiscale modelling approaches for assessing cosmetic ingredients safety, Toxicology. doi: 10.1016/j.tox.2016.05.026] Unexposed stratum corneum simply exchanges with the underlying viable skin by diffusion: where is the partition coefficient, is the total skin surface area, the fraction of skin surface area exposed, ... For the viable skin unexposed: For the skin stratum corneum exposed: for the viable skin exposed: dt(QSkin_u) and dt(QSkin_e) feed from arterial blood and back to venous blood. More complex diffusion models have been published [reference to add]. Intra-venous injection Intravenous injection is a common clinical route of administration. (to be completed) Inhalation Inhalation occurs through the lung and is hardly dissociable from exhalation (to be completed) Modelling metabolism There are several ways metabolism can be modeled. For some models, a linear excretion rate is preferred. This can be accomplished with a simple differential equation. Otherwise a Michaelis-Menten equation, as follows, is generally appropriate for a more accurate result. . Uses of PBPK modeling PBPK models are compartmental models like many others, but they have a few advantages over so-called "classical" pharmacokinetic models, which are less grounded in physiology. PBPK models can