were insufficient and research continued on physiological models . By 2010, hundreds of scientific publications have described and used PBPK models, and at least two private companies are basing their business on their expertise in this area. Building a PBPK model The model equations follow the principles of mass transport, fluid dynamics, and biochemistry in order to simulate the fate of a substance in the body . Compartments are usually defined by grouping organs or tissues with similar blood perfusion rate and lipid content (i.e. organs for which chemicals' concentration vs. time profiles will be similar). Ports of entry (lung, skin, intestinal tract...), ports of exit (kidney, liver...) and target organs for therapeutic effect or toxicity are often left separate. Bone can be excluded from the model if the substance of interest does not distribute to it. Connections between compartment follow physiology (e.g., blood flow in exit of the gut goes to liver, etc.) Basic transport equations Drug distribution into a tissue can be rate-limited by either perfusion or permeability. Perfusion-rate-limited kinetics apply when the tissue membranes present no barrier to diffusion. Blood flow, assuming that the drug is transported mainly by blood, as is often the case, is then the limiting factor to distribution in the various cells of the body. That is usually true for small lipophilic drugs. Under perfusion limitation, the instantaneous rate of entry for the quantity of drug in a compartment is simply equal to (blood) volumetric flow rate through the organ times the incoming blood concentration. In that case; for a generic compartment i, the differential equation for the quantity Qi of substance, which defines the rate of change in this quantity, is: where Fi is blood flow (noted Q in the Figure above), Cart incoming arterial blood concentration, Pi the tissue over blood partition coefficient and Vi the volume of compartment i. A complete set of differential equations for the 7-compartment model shown above could therefore be given by the following table: The above equations include only transport terms and do not account for inputs or outputs. Those can be modeled with specific terms, as in the following. Modeling inputs Modeling inputs is necessary to come up with a meaningful description of a chemical's pharmacokinetics. The following examples show how to write the corresponding equations. Ingestion When dealing with an oral bolus dose (e.g. ingestion of a tablet), first order absorption is a